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Development and validation of the quantitation of S.P.E.C.T. images for clinical applications Dixon, Katherine Louise 2005

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DEVELOPMENT AND VALIDATION OF THE QUANTITATION OF S.P.E.C.T. IMAGES FOR CLINICAL APPLICATIONS by KATHERINE LOUISE DIXON B.Sc.(Hons), The University of Edinburgh, 1996 M.Sc, The University of Exeter, 1999 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Physics) THE UNIVERSITY OF BRITISH COLUMBIA February 2005 © Katherine Louise Dixon, February 2005 A B S T R A C T The obtaining of accurate quantitative information is essential to the future development of nuclear medicine. This thesis uses three clinical quantitative measurements: tumour dosimetry, myocardial wall thickness, and myocardial infarct size, to show that accurate quantitative diagnostic information can be extracted from nuclear medicine studies. Additionally, this thesis determines the importance of comprehensive corrections for photon attenuation, photon scatter and distance-dependent resolution loss in the production of this quantitative information. Dosimetry and myocardial perfusion data sets were acquired from computer simulations, physical phantoms and clinical patients. Each data set was reconstructed using (1) filtered back-projection (FBP), (2) ordered-subset expectation maximization (OSEM), (3) OSEM plus attenuation correction (AC), (4) OSEM plus detector response compensation (DRC), (5) OSEM plus AC and DRC, and (6) OSEM plus AC, DRC and scatter correction (SC). iQuant software was developed to affectively evaluate the biodistribution of activity required for dosimetry calculations, myocardial wall thickness and myocardial infarct size. iQuant measures infarct size with exceptional accuracy and reliability, and its advantages over other myocardial quantitation software include its 3-dimensional analysis that does not require the creation of polar maps or normal heart databases. The inclusion of AC in the reconstruction process significantly improved the accuracy of tumour activity estimates (by 30%) and myocardial infarct sizes in both the inferior and septal myocardial walls (by 1% of the total myocardial volume). The inclusion of DRC produced a myocardial wall thickness closer to the truth (by 25%). AC and DRC are therefore essential for an accurate diagnostic assessment of myocardial perfusion studies and dosimetry. The addition of SC improved the accuracy of tumour activity estimates, particularly in regions with non-uniform attenuation properties (to within 5% of the truth for tumors greater than 5ml). it also provided myocardial wall thickness values closer to the truth than any other technique (10% closer than OSEM+DRC), and improved the accuracy and precision of myocardial infarct sizes (to within 0.75% of the total myocardial volume). The application of SC in addition to AC and DRC is therefore indicated in research studies involving dosimetry or myocardial infarct size, where the accuracy of measurement is essential. T A B L E O F C O N T E N T S Abstract ii Table of Contents iii List of Tables viii List of Figures xi List of Abbreviations xviii Acknowledgments xx Dedication xxi CHAPTER 1 Introduction 1 1.1 Introduction 1 1.2 Aim and motivation 2 1.3 Thesis overview 4 1.4 Role of the author 5 CHAPTER 2 Background Information and Literature Review 7 2.1 Introduction to Nuclear Medicine 7 2.2 The origin of photon attenuation, photon scatter and distance-dependent resolution loss 12 2.2.1 Photon attenuation 12 2.2.2 Photon scatter 13 2.2.3 The linear attenuation coefficient 14 2.2.4 Distance-dependent resolution loss 15 iii 2.3 Correct ions for photon attenuation, photon scatter and distance-dependent resolution loss 16 2.3.1 Attenuation correction 16 2.3.2 Scatter correction 19 2.3.3 Detector response compensat ion 21 2.3.4 Incorporating corrections in SPECT reconstruction 22 2.3.4.1 Filtered back-projection 23 2.3.4.2 Iterative reconstruct ion algor i thms 24 2.4 Clinical situations in which quantitative accuracy is important 27 2.4.1 Dosimetry 27 2.4.1.1 The clinical importance of dosimetry 27 2.4.1.2 Radioimmunotherapy - a specific clinical example 28 2.4.1.3 Internal dosimetry calculations 29 2.4.1.4 The effect of SPECT corrections on the accuracy of dosimetry 32 2.4.2 Myocardial perfusion 33 2.4.2.1 The clinical importance of myocardial perfusion imaging 33 2.4.2.2 The clinical importance of myocardial wal l th ickness 34 2.4.2.3 The clinical importance of myocardial perfusion infarct size 35 2.4.2.4 Reorientation of the heart 36 2.4.2.5 Methods used for the evaluation of myocardial detect size 37 2.4.2.6 The effect of SPECT corrections on the accuracy of myocardial perfusion measurements 40 CHAPTER 3 Methods - Creation of Data 42 3.1 Dosimetry 42 3.1.1 Introduction 42 3.1.2 Simple 2-D simulation 43 3.1.3 Comprehensive simulat ion 44 3.1.4 Phantom exper iments 46 3.2 Myocardial Wal l Thickness 50 3.2.1 Computer simulations 50 3.2.2 Phantom exper iments 51 3.2.3 Clinical data 52 iv 3.3 Myocardial Infarct Size 54 3.3.1 Computer simulations 54 3.3.2 Phantom experiments 55 3.3.3 Software validation 56 3.4 SPECT Reconstruction 58 3.4.1 Reorientation 59 CHAPTER 4 Methods - Software Design 60 4.1 ImageTools 60 4.2 iQuant - Dosimetry 61 4.2.1 The method of Dosimetry 62 4.3 iQuant - Myocardial quantitation 64 4.3.1 The method of Myocardial quantitation 64 4.4 iQuant - Removal of overlying liver from myocardial images 70 4.4.1 The method of Liver removal 70 CHAPTER 5 Methods - Quantitative Measurement 72 5.1 Dosimetry 72 5.1.1 Biodistribution calculations 72 5.1.1.1 Planar data - Simple method 72 5.1.1.2 Planar data - Complex method 73 5.1.1.3 SPECT data 74 5.1.2 System sensitivity measurement 74 5.1.3 Activity decay 74 5.1.4 Comparison to the truth 75 5.1.5 Statistical analysis 75 5.2 Myocardial Wall Thickness 76 5.2.1 Statistical analysis 77 5.3 Myocardial Infarct Size 78 5.3.1 iQuant 78 5.3.1.1 Boundary condition thresholds 78 5.3.1.2 Accuracy 78 5.3.1.3 Reliability 78 5.3.1.4 Comparison with other myocardial quantitation program 79 5.3.2 Statistical analysis 79 v CHAPTER 6 Results and Discussion 81 6.1 Dosimetry 81 6.1.1 Simple 2D simulation 81 6.1.2 Comprehensive simulation 82 6.1.3 Phantom experiments 83 6.1.4 Discussion 87 6.2 Myocardial Wall Thickness 89 6.2.1 Results 89 6.2.2 Discussion 100 6.3 Software Validation 104 6.3.1 Boundary condition thresholds 104 6.3.1.1 Threshold suggested from myocardial wall thickness studies 104 6.3.1.2 Threshold determined from myocardial infarct size studies 104 6.3.2 iQuant accuracy 108 6.3.3 iQuant reliability 109 6.3.4 Comparison to established myocardial quantitation programs 109 6.3.4.1 Comparison with Mayo Clinic software 109 6.3.4.2 Comparison with 4D-MSPECT software 111 6.3.5 Discussion 113 6.4 Myocardial Infarct Size 117 6.4.1 Phantom experiments 117 6.4.2 Clinical data 123 6.4.3 Discussion... 124 CHAPTER 7 Conclusions 126 CHAPTER 8 Future Work 129 8.1 Improving, extending and developing experiments 129 8.2 Moving iQuant in to the clinical arena 130 8.3 The further investigation of liver activity 132 Bibliography 133 vi Appendix A A1 Parameter details for MCAT body 150 A2 Parameter details for MCAT heart 152 A3 Parameter details for MCAT myocardial infarcts 154 Appendix B B1 Operating instructions for iQuant Dosimetry 156 B2 Operating instructions for iQuant Myocardial Quantitation 161 B3 Additional general instructions for iQuant 168 B4 Operating instructions for iQuant Liver Removal 175 Appendix C Additional graphs for myocardial infarct size analysis of phantom data 180 vii L I S T O F T A B L E S 3.1 Organ activity concentrations used within the MCAT phantom 44 3.2 Activity of T c 9 9 m sodium pertechnetate administered to Thorax and Jaszczak phantoms.... 47 6.1 Relative difference between the true tumor activity and that estimated from the arithmetic and geometric means of planar acquisitions derived from the 2-D simulation 81 6.2 Tumor activity estimated from planar and SPECT acquisitions of the thorax simulation 82 6.3 Relative difference between the true tumor activity and that estimated from planar and SPECT acquisitions of the thorax simulation 83 6.4 Tumor activity estimated from the complex calculations of static planar and whole body planar acquisitions of the Thorax and Jaszczak phantoms 83 6.5 Relative difference between the true tumor and hot sphere activity and that estimated from static planar and whole body planar acquisitions of the Thorax and Jaszczak phantoms 84 6.6 Tumor and hot sphere activity estimated from SPECT acquisitions of the Thorax and Jaszczak phantoms reconstructed with different techniques 85 6.7 Relative difference between the true tumor and hot sphere activities and those estimated from SPECT acquisitions of the Thorax and Jaszczak phantoms 86 6.8 The effect of reconstruction technique on the average myocardial wall thickness (Mki) of phantom and clinical data, for thresholds of 45% and 50%. Results presented ± their standard deviation 89 6.9 The average myocardial wall thickness of clinical data from male and female patients. Results presented ± their standard deviation 91 6.10 The average myocardial wall thickness of clinical data with and without the presence of liver interference. Results presented ± their standard deviation 92 6.11 The average myocardial wall thickness of stress and rest studies. Results presented ± their standard deviation 93 6.12 The average myocardial wall thickness of clinical stress data, comparing the use of treadmill and pharmacological stressing techniques. Results presented + their standard deviation 94 6.13 The average myocardial wall thickness of phantom data, comparing different myocardium to background activity ratios (3:1, 4:1, 7:1). Results presented + their standard deviation 95 viii 6.14 The average myocardial wall thickness of simulated data, comparing beating and static heart models. Results presented ± their standard deviation 96 6.15 The average myocardial wall thickness of phantom data, comparing acquisitions with and without a zoom. Results presented + their standard deviation 97 6.16 The effect of spatial filters on the average myocardial wall thickness of the phantom. Results presented + their standard deviation 97 6.17 The effect of spatial filters on the average myocardial wall thickness of clinical data. Results presented ± their standard deviation 98 6.18 Effect on the average myocardial wall thickness of the phantom, of interpolating data from 128 x 128 x 128 data sets onto 256 x 256 x 256 matrices. Results presented ± their standard deviation 99 6.19 Summary of wall thickness measurement comparisons of patient, acquisition and post-reconstruction processing parameters. From these results the requirement for a separate normal heart database for myocardial quantitation is predicted 101 6.20 The number of holes that appear in the viable myocardium VOI of normal clinical data sets 104 6.21 Threshold that produce the myocardial infarct size measurements closest to the truth for different sizes and location of infarct in the phantom 105 6.22 Thresholds that produce the myocardial infarct size measurements closest to the truth for different activity concentrations of the small, inferior infarct in the phantom 105 6.23 Thresholds that produce the myocardial infarct size measurements closest to the truth for the small, inferior infarct in the phantom containing a close lying, active liver 106 6.24 Thresholds that produce the myocardial infarct size measurements closest to the truth for different interpolations of the inferior infarcts of the phantom. All reconstructed with OSEM+AC+DRC 106 6.25 Threshold that produce the myocardial infarct size measurements closest to the truth for different locations of the medium infarct in the static and beating heart simulations 106 6.26 The threshold used for measurement of myocardial infarct size in iQuant...: 107 6.27 Reliability study, 3 independent observers measurement of myocardial infarct size from 5 identical phantoms. Infarct placed in the inferior wall and 5.3% ofthe total myocardium in size 109 6.28 Myocardial infarct size of the solid insert phantom, measured by the Mayo Clinic and using iQuant 110 ix 6.29 The parameters of linear regression analysis performed on the Mayo Clinic and iQuant measurements of myocardial infarct size 111 6.30 Myocardial infarct size measurement from clinical data reconstructed with FBP 112 6.31 The slopes of the linear regression analysis carried out on 5 measurements of 3 sizes of myocardial infarct size (phantom data). The errors in the slopes were calculated as part of the linear regression analysis. A slope of greater than 1.0 shows an overestimation in infarct size and a slope of less than 1.0 shows an underestimation 120 6.32 The correlation coefficients (R2) of the linear regression analysis carried out on 5 measurements of 3 sizes of myocardial infarct size (phantom data) 121 6.33 Comparison of the slopes of linear regression analysis and unity, the ideal slope, s for a significant difference and x for no significant difference (p=0.05). An x is therefore the ideal result for a good quantitative reconstruction technique 121 6.34 Comparison of the slopes of linear regression analysis between infarcts in different locations, s for a significant difference and x for no significant difference (p=0.05). An x is therefore the ideal result for a good quantitative reconstruction technique 122 6.35 Absolute difference between the truth and the infarct size of the phantom determined from different reconstructions, averaged over small, medium and large infarcts. The stated errors are the Confidence Intervals of 95% 122 6.36 Myocardial infarct size measurements from OSEM+AC+DRC and FBP reconstructions of clinical data 123 x L I S T O F F I G U R E S 2.1 The simplified schematic of a gamma camera. The paths of four photons, originating in an organ of interest within the body, are shown. Photon (a) is not normal to the collimator and is therefore absorbed by it. Photons (b), (c) and (d) are normal to the collimator and therefore transmitted through it, they are subsequently absorbed by the Nal(TI) crystal. Photons (b) and (c) are primary (unscattered) photons which have maintained their original energy and therefore pass through the signal processor. Photon (d) is a scattered photon with lower energy due to its change in direction, it may be therefore rejected by the signal processor. Only photons (b) and (c) reach the data processing, display and storage unit. The location of the analogue to digital converter is dependent upon the age of the camera and its manufacturer 8 2.2 SPECT acquisition and reconstruction, detailing the acquisition of 5 projections of the myocardium over 180°. In a routine myocardial scan, 64 projections are acquired over 180° 10 2.3 The extraction of 2-D slices from 3-D data sets 11 2.4 The affect of photon attenuation, photon scatter and distance-dependence resolution loss on a nuclear medicine acquisition 121 2.5 The photoelectric affect. Energy of each photon or electron (e") written in brackets 13 2.6 (a) Compton scatter, and (b) Rayleigh scattering. Energy of each photon or electron (e) written in brackets 13 2.7 Measurement of (a) the narrow beam, and (b) the broad beam linear attenuation coefficients 15 2.8 Transmission source designs for Gd 1 5 3 , (a) collimated sheet source, (b) line source at central focus of fan beam collimator, and (c) line source with asymmetric fan beam collimator, (d) High energy Ba 1 3 3 line source with septal penetration of high energy photons through parallel beam collimator 17 2.9 The Profile transmission system (a) source design, (b) photon flux emitted by transmission source, and (c) photon flux reaching camera after being attenuated by the body 18 2.10 The process of filtered back-projection in 2-D 23 xi 2.11 Dosimetry involves the measurement of radiation dose to each organ from radiation emitted by the organs that take up the radiopharmaceutical. In this particular example a radiopharmaceutical designed to image the liver is also taken up by the lungs. The dose to the lungs will depend upon the amount of radiation emitted in both the lungs and the liver, the dose to the liver will depend upon the amount of radiation emitted in the liver and the lungs. Also important is the dose to the kidneys which lie close to the liver and are very sensitive to radiation, these are the critical organs for this particular test 28 2.12 Presentation of the myocardium of the left ventricle after reorientation 36 2.13 (a) Definition of short axis slice through LV myocardium used to (b) create circumferential profile plotted onto polar map 37 3.1 Transaxial body slice with five tumor locations, used in the 2-D study 43 3.2 The Siemens convention for camera position. View facing the dual headed Siemens E-cam camera (the SimSET detector only has one head) 45 3.3 The end view (from the head of the bed) of the Jaszczak phantom showing the positioning of the hot spheres and their numbering 46 3.4 Positioning of the water bags on the Thorax phantom 47 3.5 The Jaszczak and Thorax phantoms set up on the scanning bed 48 3.6 Locations of MCAT phantom medium infarct (13.9% of total myocardium) 54 4.1 Set-up window of the Dosimetry function in iQuant, showing the cursors positioned in the centre of the tumor 62 4.2 A 3-D surface rendering of a tumor VOI 63 4.3 The set-up window of the Myocardial Quantitation function in iQuant, showing the cursors positioned in the centre of the left ventricle 65 4.4 A 3-D surface rendering of a region grown from a point in the myocardium, using 50% of the maximum voxel counts in the entire data set as the stopping criteria. The myocardium and the close lying liver have been included in the region 65 4.5 A 3-D surface rendering of a region grown from a point in the myocardium, using 60% of the maximum voxel counts in the entire data set as the stopping criteria. Only the LV myocardium has been included in the region 66 4.6 The position of wall thickness measurements taken from a short axis slice of the LV myocardium 67 4.7 The display window of the Myocardial Quantitation function in iQuant, showing a short axis slice of the myocardium and close lying liver 68 xii 4.8 The steps involved in iQuant to determine the viable and complete LV VOIs of a data set from the static MCAT phantom with an infarct in the lateral wall. Steps are depicted for a horizontal long axis slice (left hand column), and a short axis slice (right hand column) 69 4.9 The calculation window of the Myocardial Quantitation function in iQuant, showing a short axis image of the original data set (left) and the same image with the liver removed (right) 71 6.1 Myocardial wall thickness of phantom data comparing the quantitation of reconstruction techniques for the thresholds of 45% and 50% 90 6.2 Myocardial wall thickness of clinical data comparing the quantitation of reconstruction techniques for the thresholds of 45% and 50% 90 6.3 Myocardial wall thickness of clinical data reconstructed using OSEM+AC+DRC, comparing male and female patients 91 6.4 Myocardial wall thickness of clinical data reconstructed using OSEM+AC+DRC, comparing data with and without the presence of liver interference 92 6.5 Myocardial wall thickness of clinical data reconstructed using OSEM+AC+DRC, comparing rest and stress studies 93 6.6 Myocardial wall thickness of clinical data reconstructed using OSEM+AC+DRC, comparing treadmill and pharmacologicaFpatient stressing techniques 94 6.7 Myocardial wall thickness of phantom data reconstructed using OSEM+AC+DRC, comparing myocardium to background ratios of 7:1, 4:1 and 3:1 95 6.8 Myocardial wall thickness of simulation data reconstructed using OSEM+AC+DRC, comparing a static and beating model heart 96 6.9 Myocardial wall thickness of phantom data, reconstructed using OSEM+AC+DRC, comparing the affect of spatial filters 98 6.10 Myocardial wall thickness of phantom data reconstructed using OSEM+AC+DRC, comparing original and interpolated matrix sizes for all thresholds 99 6.11 Infarct size determined with iQuant of the original MCAT model with a beating heart. The black column represents the true average volume of the infarct and the bar extending from the column represents the change in volume seen during the cardiac cycle. Each grey column represents the mean ± SD of a series of four measurements .... 108 6.12 Linear regression analysis carried out on the Mayo Clinic measurements of myocardial infarct size, on the phantom containing solid infarct inserts, reconstructed with FBP 110 6.13 Linear regression analysis carried out on the iQuant measurements of myocardial infarct size, on the phantom containing solid infarct inserts, reconstructed with FBP 111 xiii 6.14 The partial volume affect on the myocardial wall 114 6.15 4D-MSPECT polar map showing the genuine apical infarct and the appearance of basal shortening of the septal wall as a second infarct 116 6.16 Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 117 6.17 Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 118 6.18 Linear regression analysis carried out on OSEM+AC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 118 6.19 Linear regression analysis carried out on OSEM+DRC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 119 6.20 Linear regression analysis carried out on OSEM reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 119 6.21 Linear regression analysis carried out on FBP reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 120 B1.1 Main window 156 B1.2 Open file window 156 B1.3 Dosimetry region selecting window 157 B1.4 Dosimetry threshold window 157 B1.5 Dosimetry display window - background VOI 158 B1.6 Dosimetry VOI information box 159 B1.7 Dosimetry display window - tumor VOI 159 B1.8 Surface rendering of tumor VOI 160 B2.1 Cursor placed in centre of left ventricle 161 B2.2 Cursor placed in myocardium 161 B2.3 3D region growing box 161 B2.4 Surface rendering of (a) myocardium and liver, (b) myocardium alone 162 B2.5 iQuant threshold window 163 B2.6 iQuant display window 163 xiv B2.7 Surface rendering of viable myocardium VOI 164 B2.8 Surface rendering of total myocardium VOI 165 B2.9 VOI information select box 165 B2.10 VOI information box 166 B2.11 Surface rendering of viable myocardium and infarct 166 B3.1 Main window 168 B3.2 Region selecting window 170 B3.3 Threshold window 171 B3.4 Display window 172 B3.5 VOI loading window 174 B4.1 Cursor placed in centre of left ventricle 175 B4.2 Cursor placed in myocardium 175 B4.3 3D region growing box 175 B4.4 Surface rendering of (a) myocardium and liver, (b) myocardium alone 176 B4.5 Liver removal threshold window 176 B4.6 Liver removal display window 177 B4.7 Liver removal VOI selection box 178 B4.8 Liver removal output window 179 C.1 Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 180 C.2 Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R 2 180 C.3 Linear regression analysis carried out on OSEM+AC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 181 C.4 Linear regression analysis carried out on OSEM+DRC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 181 xv C.5 Linear regression analysis carried out on OSEM reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 182 C.6 Linear regression analysis carried out on FBP reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 182 C.7 Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 183 C.8 Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 183 C.9 Linear regression analysis carried out on OSEM+AC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 184 C.10 Linear regression analysis carried out on OSEM+DRC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 184 C.11 Linear regression analysis carried out on OSEM reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 185 C.12 Linear regression analysis carried out on FBP reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 185 C.13 Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R 2 186 C.14 Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 186 C.15 Linear regression analysis carried out on OSEM+AC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 187 C.16 Linear regression analysis carried out on OSEM+DRC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 187 xvi C.17 Linear regression analysis carried out on OSEM reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 188 C.18 Linear regression analysis carried out on FBP reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2 188 xvii L I S T O F A B B R E V I A T I O N S AC photon attenuation correction in SPECT. APD analytical photon distribution, method of SPECT scatter correction. APDI APD interpolation, method of SPECT scatter correction. CAD coronary artery disease, which affects the blood flow to the heart muscle. Cl confidence interval, the range of values that have a (for example) 95% chance of containing the mean value of the entire population. CT computer tomography, 3-D diagnostic imaging technique. DRC detector response compensation, correction for distance-dependent resolution loss in SPECT. ECG electrocardiography, measurement of the electrical signal of the heart. FBP filter back-projection, simple SPECT reconstruction technique. FWHM ... full-width at half-maximum, method used to measure spatial resolution. GPSF geometric point spread function, the function describing the relationship between a point source and the image of the point source; due to system geometry. GUI graphical user interface, window based software. LEHR low energy, high resolution collimator for gamma camera, used to image 9 9 m T c for dosimetry applications. LEUHR .. low energy, ultra high resolution collimator for gamma camera, used to image 9 9 m T c for myocardial perfusion studies. LV left ventricle of the heart. MAb monoclonal antibody, a protein designed to neutralise an antigen expressed on a tumor cell. ME medium energy collimator for gamma camera, used to image 1 1 1 ln. Ml myocardial infarction, permanently damaged heart muscle. MIRD The Medical Internal Radiation Dose Committee of the Society of Nuclear Medicine. MIRG Medical Imaging Research Group at Vancouver General Hospital. MLEM.... maximum likelihood expectation maximization, iterative SPECT reconstruction technique. MRS magnetic resonance spectroscopy, diagnostic technique. Nal(TI).... Sodium Iodide doped with Thallium, material from which a gamma camera crystal is made. OSEM.... ordered subset expectation maximization, iterative SPECT reconstruction technique. PET positron emission tomography, 3-D diagnostic imaging technique closely related to SPECT. PHA pulse-height analyser, used to define the energy window of a gamma camera acquisition. PMT photomultiplier tube, converts and amplifies the light signal emitted from the gamma camera crystal into an detectable electrical signal. xviii RIT radioimmunotherapy, a therapy technique which utilizes the ablative properties of radiation by delivering radioactive particles directly to the tumor cells. ROI region of interest, area of an image that contains the pixels depicting (for example) a tumour. RV right ventricle of the heart. SC photon scatter correction in SPECT. SPECT... single photon emission computer tomography, 3-D diagnostic imaging technique. SPSF scatter point spread function, the function describing the relationship between a point source and the image of the point source, due to photon scatter. VOI volume of interest, 3-D region of interest. xix A C K N O W L E D G M E N T S My greatest thanks go to Anna Celler, my supervisor whose straight forward and welcoming manner persuaded me to travel across the world to work with her. She has constantly been encouraging, supportive and enthusiastic, even when life was not quite so easy. This work would not have been possible without the support of the other members of MIRG. My thanks go especially to Stephan whose knowledge of computers, collimator blurring corrections and SPECT reconstruction techniques, at times seemed limitless. And to Eric, the master of MCAT and SimSET, and the controller of all scatter correction. This work would have taken longer without the help of Mike, Bernard and Lesley, co-op students working under my supervision at MIRG. Mike was responsible for the code in the first version of ImageTools, and Bernard was responsible for the code in our first attempt at myocardial perfusion infarct size measurement with iQuant. Lesley mastered the attenuation map simulation program and spent many happy hours measuring myocardial infarct sizes. My thanks to all of them. My thanks go to the members of my PhD committee for their time, support and patience, and in particular Dr Fung who shared a portion of his cardiac brain with me and Prof Axen who spent many hours working on incomprehensible dynamic data. My thanks also go to Prof Ronald Harrop for his well honed reading skills. The statistical analysis included in this thesis would not have been possible without discussions with Michael Schulzer and Dave's knowledge of SPSS. The use of 4D MSPECT software would not have been possible without the assistance of Ed Ficaro. My thanks also go to Lori, Craig and the multitude of other nuclear medicine technicians whom I bothered relentlessly, requesting camera time and radioactivity. Also to Mike King and Hennie Pretorius who graciously allowed me to use their patient database for work that eventually proved to be uninformative at the present time. And finally my thanks go to my Canadian friends, Catherine, Marie-Laure, Peter, Tonia and Vicki (alphabetical order folks), who kept me sane. And to Sue and Peter Ross, my Canadian family. xx D E D I C A T I O N To my Edinburgh clan who I seriously missed when I went to Canada. To my family who managed to support me across an ocean. And of course, to Terry, my soul mate. xxi 1 C H A P T E R 1 I N T R O D U C T I O N 1.1 Introduction Nuclear medicine is an imaging technique capable of investigating the physiology of the human body. A radioactive tracer is injected into the body and images of the tracer distribution are acquired on a large aperture camera. The camera can be moved around the body, acquiring images (projections) from numerous angles. These 2-D projections can be reconstructed to form a 3-D map (data set) of the tracer distribution in the body. This process is known as single photon emission computer tomography (SPECT). The radioactive tracer is designed in such a way that its distribution within the body is indicative of a specific physiological process. In this way physicians can determine the presence of cancer in the bones, or blood clots in the lungs; they can study the dynamics of the filtering system in the kidneys, or the efficiency of the heart. Presently, in the majority of cases, such clinical studies are analysed qualitatively, by visual interpretation of the images., There are many situations where the accurate determination of quantitative information would greatly enhance the diagnostic value of the nuclear medicine study. Ideally, such analysis involves the quantitative (and dynamic) estimation of the amount of tracer in a given organ relative to its concentration circulating in the blood system (measured, for example, from blood samples). This level of quantitative analysis requires accurate information on the amount of tracer in a given location and also its volume; both values must be obtained from the nuclear medicine data set. The accuracy of these measurements have to be validated in the clinical environment. This thesis will focus on two specific clinical applications of nuclear medicine where the acquisition of accurate quantitative information is essential: dosimetry and myocardial perfusion imaging. Although the discussion will focus on these two situations, the results and conclusions are applicable and can be extended to many other nuclear medicine investigations. Dosimetry is the measurement of the radioactive dose administered to a specific region of the body. Whether the dose is administered for therapeutic or diagnostic reasons, its accurate measurement is essential for the efficient treatment of tumors and the development of new nuclear medicine techniques. Myocardial perfusion imaging is the study of the blood flow to the muscle of the heart. It is used to assess the extent and severity of coronary artery disease (CAD), and thereby aid in the formulation of a treatment plan specific to an individual patient. Accurate quantitation of myocardial perfusion is required Chapter 1: Introduction 2 to measure the severity and extent of myocardial defects, thereby providing an essential research tool to determine the relative effectiveness of different therapies. The accuracy of quantitative information derived from nuclear medicine acquisitions is limited by a number of physical factors. These factors include the attenuation and scatter of photons (rays of radiation) as they pass through the body, and the loss of spatial resolution in the images caused by the collimator, which is an essential part of the camera's detector. These factors not only destroy the quantitation of the data, but they can also dramatically alter the appearance of the image, introducing substantial artefacts. Although routine, these artefacts often go unrecognised, degrading the possible diagnostic capabilities of nuclear medicine. In the past various techniques for the correction of these inhibiting factors in SPECT data sets have been suggested and investigated. However, only recently have techniques been developed that could perform the more complicated corrections. Correction for photon attenuation in myocardial perfusion studies is now well established in large clinical centres. Only a few manufacturers offer software to correct for resolution loss and it is seldom used. Only simple approximate methods are available for the correction of photon scatter as the computational time involved in more elaborate corrections is considered prohibitive in the routine clinical environment. The Medical Imaging Research Group (MIRG) at Vancouver General Hospital have developed a comprehensive set of corrections that differ from those developed elsewhere in significant ways, and can be implemented in a single algorithm. The ability of these corrections to produce accurate quantitative information must be rigorously tested under challenging clinical conditions. 1.2 Aim and motivation The hypothesis of this thesis is that the comprehensive set of corrections for photon attenuation, photon scatter and distance-dependent resolution loss, developed at MIRG, will allow suitably accurate quantitative information to be gathered from clinical data sets. Once it has been shown that accurate quantitative data can be extracted from clinical acquisitions, nuclear medicine can stride headlong into numerous fields of research and development. Accurate quantitative imaging will open the door for amazing opportunities in the fields of cancer therapy, physiological measurement and molecular imaging. Quantitative information is numerical information; the amount of radiation emitted by a radioactive substance taken up by a tumor, the thickness of a myocardial wall, or the size of a myocardial perfusion defect. It can be an absolute measurement taken directly from the data set, as in these first two examples. It can also be a relative measurement, a comparison of one quantity with another, as in the case of myocardial infarct size where the size of the infarct (an irreversible defect) is reported as a percentage of the size of the complete myocardium. Whichever method of measurement is used, the gathering of accurate quantitative information is essential in many situations. The quantitative information required from the data set of a nuclear medicine dosimetry study is the amount of radiation emitted by the radioactive substance that was taken up by the tumor (tumour Chapter 1: Introduction 3 activity) or other organ of interest. This information, together with knowledge of the structure of the body and the properties of the radiation, is used to calculate the radiation dose (the amount of energy absorbed by the tissue), and therefore to estimate the possibility of radiation damage to the tissue. Present calculations performed from 2-D planar studies (single images) can provide tumour activity estimates that are out by a factor of 3. The variation in results from both planar and SPECT studies is also highly dependent upon the position of the tumour within the body. A technique that would allow tumour activity to be measured consistently to within 5% of its true value, irrespective of its position within the body, would have a significant clinical impact on nuclear medicine therapy and a massive impact on therapeutic and diagnostic research. It would also substantially affect the accuracy of the diagnosis and staging of tumours. To test new treatments for Myocardial Infarction (Ml) against standard methods, a measure is required that would predict the mortality of patients undergoing each treatment. Myocardial infarct size, as measured from myocardial perfusion studies, has been shown to provide such a prediction. However, due to the quality of treatments presently available, even if the new technique improves upon the standard one, the differences reflected in myocardial infarct size will be small. It is therefore imperative that the quantitative measurement of myocardial infarct size is accurate. Presently the measurement of an 18 ml infarct in the inferior myocardium wall from a SPECT data set reconstructed with no corrections can be out by 50%. The measurement of the same infarct from a data set reconstructed with attenuation correction can still be out by 20%. A technique that consistently measures myocardial infarct size to within 5% of its true value would have a significant affect on the prognostic value of this measurement. A small reduction in infarct size seen in a clinical trial would have a considerable impact on the large patient population that would be affected by an alteration in Ml treatment. With a measurement known to be this accurate, clinical trials could be carried out with a higher statistical power, or using smaller patient cohorts thus reducing both the cost and the time required. For routine myocardial perfusion studies, clinical reports provide only an estimate of the size of any perfusion defect. A technique that measures myocardial infarct size to within 10% of its true value regardless of its location would therefore have a significant diagnostic impact. Myocardial wall thickness provides a global measure of the accuracy of myocardial perfusion images, giving an indication of the degrading affects of photon attenuation, photon scatter and distance-dependent resolution loss. Although the accuracy with which myocardial wall thickness can be measured has no direct clinical impact, the accurate measurement of this and the previous parameter would provide evidence of the removal of the numerous artefacts seen in myocardial perfusion images. As myocardial wall thickness is of the same order of magnitude as the spatial resolution of a SPECT data set, it will not be possible to accurately reconstruct its size. However, it will be possible to determine if it lies closer to or further from the truth, and it is the only parameter discussed in this thesis which can be determined for clinical data sets as well as phantom data sets. Chapter 1: Introduction 4 Therefore, the aim of this thesis is to use these three quantitative measurements to show that accurate quantitative diagnostic information can be extracted from nuclear medicine studies; and to determine the importance of each of the MIRG corrections for photon attenuation, photon scatter and distance-dependent resolution loss in the production of this quantitative information. 1.3 Thes is ove rv iew To aid the reader in the understanding of this thesis, the following section has been included briefly describing the contents of each chapter. Chapter 2 provides background information to the thesis with an extensive literature review. A brief description of SPECT and an introduction to the relevant technical vocabulary are followed by a description of the physical processes that inhibit the acquisition of accurate quantitative data. The methods used to rectify these problems are discussed with particular emphasis on the correction techniques developed by MIRG. This chapter also contains a detailed description of the clinical situations where the diagnostic value of SPECT studies would be significantly improved by the provision of accurate quantitative information. Chapter 3 details the methods used to carry out experiments. Data sets were collected from computer simulations, physical phantoms and clinical studies. The experiments were designed either to allow the measurement of the biodistribution of activity and hence give an indication of the quantitation of dosimetry, or to allow the measurement of myocardial wall thickness or myocardial infarct size and hence the quantitation of myocardial perfusion studies. Details of the reconstruction of SPECT projections are also covered. Chapter 4 introduces iQuant, the software developed to measure the quantitative parameters specific to dosimetry and myocardial perfusion imaging. Chapter 5 discusses the procedures used to measure the biodistribution of activity from planar and SPECT acquisitions. The methods involved in determining suitable myocardial boundary conditions and the reliability and accuracy of iQuant are included in this chapter. Additionally, the statistical tests performed to analyse the measurements of tumor activity, myocardial wall thickness and infarct size are described. Chapter 6 presents the results of quantitative measurements of dosimetry, myocardial wall thickness and myocardial infarct size. This chapter also provides discussion on the ability of these findings to determine the clinical importance of the SPECT corrections. Chapter 7 summarizes the findings of the investigations and the conclusions that have been drawn. Chapter 8 discusses the possible continuation of this work together with suggestions of experiments and alternative image quantitation methods. The adaptation of the research tool iQuant into a clinical software format is also discussed. Chapter 1: Introduction 5 1.4 Role o f the au tho r The work submitted in this thesis was performed by myself as detailed below. The contribution of others is also detailed here. My task was to determine if accurate quantitative diagnostic information could be extracted from clinical nuclear medicine studies with the use of corrections for photon attenuation, photon scatter and distance-dependent resolution loss. Study design: • I performed the preliminary studies (not included in this thesis) to visualize, evaluate and quantify variations observed in clinical myocardial perfusion SPECT images reconstructed using different techniques. I developed the concept and design of the ImageTools software to perform these comparisons (the code was written by a co-op student). • Based on these results and an extensive literature review, I formulated the concept of this thesis. I developed and designed the structure of the work to be performed, specifying the cases to be studied, the number of simulations and phantoms to be performed in each case, and the measurements to be taken. • I researched currently available software packages for myocardial quantitation, and recognized the problems associated with their approaches and the need to develop software capable of performing these measurements in a three-dimensional environment. • I designed the statistical analysis to be performed on the collected results (in collaboration with a clinical statistics professor). Collection of data: • I produced all computer models and performed all computer simulated acquisitions. • I performed all phantom studies discussed in this work with the exception of the Mayo Clinic comparison experiment (carried out by a nuclear medicine technician). • I retrieved all clinical data from the archives of the nuclear medicine department (a student nurse obtained consent from all patients). Before the majority of the clinical data was collected I performed statistical power calculations to determine the number of clinical cases required to produce significant results. • I reconstructed all data sets. Software Design: • I developed the concept and design of the iQuant software to perform measurements of tumour activity, myocardial wall thickness and myocardial infarct size. • I wrote the majority of the new iQuant code (based on two co-op student projects). • I performed extensive tests to determine the most suitable boundary conditions to delineate viable myocardial tissue for the measurement of myocardial infarct size. Chapter 1: Introduction 6 • To validate the use of iQuant to measure myocardial infarct size, I tested its accuracy and reliability (using two co-op students as additional observers in this latter study). I also performed comparisons with other myocardial perfusion quantitation software. Quantitative measurement: • I performed all the quantitative measures and the statistical analysis reported in this thesis. 7 C H A P T E R 2 B A C K G R O U N D I N F O R M A T I O N A N D L I T E R A T U R E R E V I E W 2.1 I n t roduc t ion to Nuclear Medic ine Nuclear medicine is no longer the only imaging modality that can provide diagnostic information on the physiological processes of the human body. Positron Emission Tomography (PET), Magnetic Resonance Spectroscopy (MRS), contrast Computer Tomography (CT) and Ultrasound each now have a significant role. Nuclear medicine is however the most well established method, providing an essential asset to the armoury of diagnostic examinations. The key element in nuclear medicine is the radioactive tracer (radiopharmaceutical); made up of a radioisotope and a pharmaceutical, both specific to their task. The isotope emits gamma photons (y photons) with energy high enough for a large proportion of the radiation to exit the body but energy low enough to be stopped by the detector. The isotope must also be relatively easy to produce and simple to attach to the pharmaceutical. The most commonly used radioisotope is Technetium-99m (99mTc), with y photon energy of 140 keV; which fits all of the above criteria. The pharmaceutical is particular to the diagnostic test required, and is designed to provide information on a specific biological process. For example, Sestamibi is a pharmaceutical designed to provide information on the perfusion (blood flow) in the myocardium (the muscle of the heart). When the pharmaceutical has been labelled with the radioisotope, forming a radiopharmaceutical, it is injected into the blood stream of the patient. The emitted radiation is then measured by a detector (gamma camera). The gamma camera provides information as to the location of the isotope and therefore also of the pharmaceutical. In the above example, information obtained relating to the perfusion of the myocardium is used to detect areas of decreased perfusion. This in turn will relate to significant blockages in the cardiac arteries that may require further treatment. The gamma camera (Figure 2.1) may have one, two or three heads which can be rotated around a patient to provide images (projections) from a number of angles. Alternatively the camera heads remain stationary or scan along the length of a patient providing single (planar) images. The most essential element of the camera head is the detector; in most cases this is a single crystal made of Nal(TI) (Sodium Iodide doped with Thallium), with a detection surface of approximately 50 by 40 cm and a thickness of 0.9 cm. Behind the crystal is an array of photomultiplier tubes, the associated electronics and analogue to digital converters. In front of the crystal is a collimator; which consists of a sheet of lead containing holes and lying parallel to the crystal surface. For most clinical applications a parallel hole collimator is used, containing holes that are perpendicular to the surface of the crystal (Figure 2.1). This Chapter 2: Background Information and Literature Review 8 essentially means that photons arriving at the camera face are transmitted through the collimator holes to the crystal if they are travelling normal to it (photons b, c and d, Figure 2.1), but are absorbed by the collimator if they are travelling at any other angle (photon a). As a result, only photons travelling normal to the camera head can have any influence on the image produced, providing an image directly related to the spatial distribution ofthe radiopharmaceutical that emitted the radiation. Data processing, display and storage unit Signal processor Figure 2 . 1 : The simplified schematic of a gamma camera. The paths of four photons, originating in an organ of interest within the body, are shown. Photon (a) is not normal to the collimator and is therefore absorbed by it. Photons (b), (c) and (d) are normal to the collimator and therefore transmitted through it, they are subsequently absorbed by the Nal(TI) crystal. Photons (b) and (c) are primary (unscattered) photons which have maintained their original energy and therefore pass through the signal processor. Photon (d) is a scattered photon with lower energy due to its change in direction, it may be therefore rejected by the signal processor. Only photons (b) and (c) reach the data processing, display and storage unit. The location of the analogue to digital converter is dependent upon the age of the camera and its manufacturer. The y photon emitted from the body interacts with the Nal(TI) crystal through photoelectric, Compton and/or Rayleigh scattering systems (discussed later). For a given photon energy Nal(TI) crystal thickness is selected such that the majority of y photons are totally absorbed before they reach the back surface of the detector. The resultant excited Nal molecules return to their neutral ground states by 4 photon paths Human body containing organ of interest Collimator Nal(TI) crystal Photomultiplier tubes Chapter 2: Background Information and Literature Review 9 emitting light photons; the number of which is directly proportional to the absorbed energy. The light photons travel through the crystal, and through an optical window to an array of photomulitplier tubes. Each photomultiplier tube (PMT) includes a photocathode that releases electrons when light photons are absorbed. The number of electrons released into the PMT by the photocathode is proportional to the number of light photons absorbed, and therefore proportional to the energy of the detected photon when summed over all PMTs. The inside of the PMT is a vacuum, with dynodes positioned at intervals along its length, and an anode at the opposite end to the cathode. An electric voltage is applied between each electrode: from cathode to first dynode, first dynode to second dynode,... last dynode to anode. The electrons emitted at the cathode are therefore accelerated towards the anode, via each dynode. At each dynode approximately 6 electrons are emitted for each incident electron, thus the electrical signal (number of electrons) reaching the anode is amplified to a detectable level while remaining in proportion to the original incoming y photon. The initial role of the signal processing unit is to provide information on the energy and location of the incoming photon. The energy is determined by the amplitude of the total electrical signal associated with the photon. The location is derived by analysing the signal, by comparing the relative amplitudes of signals resulting from each PMT. Gamma photons will not lose energy on their journey through the body unless scattered or absorbed. Absorbed photons do not arrive at the camera and scattered photons lose energy and change direction. The change of direction means that scattered photons incident on the camera, will appear to have come from a different location to that from which they actually originated. However, as the energy of the incoming photons can be determined from the amplitude of the electronic signal, a pulse-height analyser (PHA) can be used to select only those photons whose energies fall within specified limits. This energy 'window' is centred on the original photon energy (photopeak), known for each isotope therefore removing signals from photons scattered through the largest angles. The energy window must be of an optimal width as the system must record many photons to decrease the noise content of the image, while cutting out as many scattered photons as possible. Single photon emission computed tomography (SPECT) is the process by which a series of projections (images acquired from a number of angles around the body) are reconstructed into a three-dimensional (3-D) data set. A schematic diagram of this process is presented in Figure 2.2. The aim of the reconstruction process is to produce a 3-D representation of the original 3-D object. Chapter 2: Background Information and Literature Review 10 Acquisition of... ... 5 projections of Figure 2.2: SPECT acquisition and reconstruction, detailing the acquisition of 5 projections of the myocardium over 180°. In a routine myocardial scan, 64 projections are acquired over 180°. Chapter 2: Background Information and Literature Review 11 A standard nuclear medicine projection is made up of 64 x 64 or 128 x 128 pixels. A pixel is the smallest unit of a 2-D projection, approximately 5 mm in each dimension for a 128 x 128 pixel projection. The reconstructed 3-D data set is an estimation of the original object taken from these projections, and is made up of 128 x 128 x 128 voxels. Voxels are the 3-D equivalent of a pixel. It is difficult to comprehensively view an entire 3-D data set on a single display. A more simple approach has been devised using 2-D images (slices) extracted from the data set in any of the three dimensions (Figure 2.3). In the standard orientation these slices are in the transaxial, sagittal and coronal planes. A number of these slices can be presented on one screen side-by-side, allowing the clinician to view a sample of the complete data set. Coronal slices Transaxial slices Sagittal slices Figure 2.3: The extraction of 2-D slices from 3-D data sets. Chapter 2: Background Information and Literature Review 12 2.2 The or ig in o f p h o t o n a t tenuat ion , p h o t o n sca t te r a n d d is tance-dependen t reso lu t ion loss Many of the problems associated with the accurate quantitation of nuclear medicine images and data sets are related to the interaction of photons with matter: the attenuation and scatter of photons as they propagate through the body, and the geometry of the collimator's design which dictates the acceptance angle of each collimator hole (Figure 2.4). The following sections detail each of these interactions and the effect they have on the quality of nuclear medicine data sets. I b " ' > ^ path of an unattenuated photon path of a scattered photon, (a) and (b) • • path of an absorbed photon region in which unattenuated photons can originate and still be detected at the same point on the camera Figure 2.4: The effect of photon attenuation, photon scatter and distance-dependence resolution loss on a nuclear medicine acquisition. 2.2.1 Photon attenuation The attenuation of y photons as they pass through the human body is due to the absorption and scatter interactions between electromagnetic radiation and matter. An absorption interaction in the form of the photoelectric effect or pair production, causes the complete transfer of energy from the photon to the material through which it is passing. However, pair production only becomes significant at photon energies above 10 MeV and never occurs below an energy of 1.022 MeV. It is therefore not relevant in a discussion of nuclear medicine. Compton and Rayleigh scatter interactions cause the path of the photon to alter. No energy is transferred during a Rayleigh scatter event. In the case of Compton scatter the change in direction is accompanied by the transfer of a portion of the photon's energy to the surrounding medium. The photoelectric effect is particularly important at photon energies below 100 keV, but also needs to be considered at higher energies. The energy from the incoming photon is completely absorbed by a low orbit, bound electron. The electron escapes the atom using the equivalent of its binding energy (E B E) and the remainder of the energy is apparent as its kinetic energy (Figure 2.5). The resultant excited Chapter 2: Background Information and Literature Review 13 atom eventually decays, emitting characteristic X-rays or Auger electrons. The probability of a photon being absorbed by the photoelectric effect is greater at photon energies just above those of the electron's binding energy. The probability also varies with Z 3, where Z is the atomic number of the material, and inversely with E r 3 , where E T is the energy of the incident photon. Figure 2.5: The photoelectric effect. Energy of each photon or electron (e") written in brackets. Due to photon absorption the number of photons exiting the body is not equal to the number of photons originating within it (Figure 2.4). The number of photons originating within an organ cannot therefore be calculated directly from the number of photons accepted by the camera; the number is also dependent upon the density and thickness of the tissue through which the photons pass as they travel through the body. 2.2.2 Photon scatter Rayleigh scatter plays an important role at electromagnetic energies below 50 keV. The oscillating electric field associated with the incident photon causes the electrons in an atom to vibrate. They in turn emit radiation of the same wavelength and therefore the same energy as the incident photon. The direction in which these scattered waves constructively interfere is the new direction of the resultant photon (Figure 2.6a). This is an elastic interaction; a change in direction without a change in energy. Figure 2.6: (b) Rayleigh scattering, and (a) Compton scatter. Energy of each photon or electron (e) written in brackets. Chapter 2: Background Information and Literature Review 14 Compton scatter is significant at electromagnetic energies between 100 keV and 10 MeV. The incoming photon interacts with an unbound or weakly bound orbital electron giving up a portion of its energy to that electron. The electron moves off with a kinetic energy equal to that lost by the photon, and due to the conservation of momentum, the photon also changes course (Figure 2.6b). A 140 keV photon Compton scattered through 45° will only lose 7.4% of its energy and will hence be accepted by the camera's 20% energy window centred on the 140 keV photo-peak [1]. Therefore photons accepted by the camera may not have originated at the point from which they appear to have come. Photons originating in neighbouring organs may scatter in the tissue of an organ of interest, falsely increasing the number of photons that appear to originate in that organ (Figure 2.4, photon (a) originating in the liver and scattering in the heart). Photons originating in an organ of interest may scatter in the body, falsely increasing the number of photons that appear to originate in the background tissue (Figure 2.4, photon (b) originating in the heart, scattering in the body and falling within the acceptance angle of the collimator). The distribution of scattered photons in an image is therefore related to the distribution of activity within the body, in addition to the density and thickness of the tissue through which the photons travel. 2.2.3 The linear attenuation coefficient In materials with low Z numbers, such as those found in the body, and at photon energies associated with the common nuclear medicine isotopes ( 9 9 mTc emits photons with an energy of 140 keV), Compton scatter and the photoelectric effect are the dominant interaction processes. However, contributions from all three interactions produce the attenuation properties of the medium. For each photon energy incident on a material of given density, the attenuation properties of that material due to a particular interaction can be described by an attenuation coefficient; npe , psc and pn for the photoelectric effect, Compton scatter and Rayleigh scatter, respectively. The sum of these coefficients is the linear attenuation coefficient, p, which describes the absolute attenuation properties of the material: M = MPe+Mcs+Mrs (2-1) With N0 photons incident on a material of thickness x, the number of photons N that will exit the material is: N = (2.2) The linear attenuation coefficient described above is the narrow beam linear attenuation coefficient. As used equation 2.2 it predicts r N ^ the proportion of incident photons that will not interact with the material in any way (by absorption or scatter). This coefficient can be measured by detecting only those photons that exit the material at the same angle as they entered it, using the experimental set-up shown in Figure 2.7a. A second, broad beam form of the linear attenuation coefficient can be used in equation Chapter 2: Background Information and Literature Review 15 2.2 to predict the proportion of incident photons that will actually exit a material, and therefore 1 the proportion of photons that will be completely absorbed by the material. The broad beam linear attenuation coefficient can be measured by detecting all photons that exit the material (Figure 2.7b). (a) incident photons -> -> -> transmitted photons —--> I I attenuating medium radiation thin detector slit (b) incident photons transmitted photons I attenuating medium | radiation thick detector slit Figure 2.7: Measurement of (a) the narrow beam, and (b) the broad beam linear attenuation coefficients. 2.2.4 Distance-dependent resolution loss Due to the finite angular acceptance of a collimator, photons incident on the camera crystal do not necessarily originate along the line projected through the body perpendicular to the crystal face. The photons can originate from anywhere within a cone, whose apex is sited on the surface of the crystal and whose apical angle is determined by the diameter of the collimator holes and the thickness of the collimator (see Figure 2.4). The probability of photon distribution across the diameter of the cone (parallel to the crystal face) is approximately a Gaussian distribution. This phenomenon, entirely defined by the collimator geometry, causes a loss in spatial resolution which increases with distance from the crystal. It is therefore known as distance-dependent resolution loss. Chapter 2: Background Information and Literature Review 16 2.3 Corrections for photon attenuation, photon scatter and distance-dependent resolution loss 2.3.1 Attenuation correction For even the most simple method of attenuation correction (AC), information is required concerning the attenuation properties of the body. In the original Chang method [2], the body is assumed to be composed of water with a uniform linear attenuation coefficient. The counts obtained from each depth in the body can therefore be multiplied by a suitable factor to compensate for the count degradation caused by this attenuation. With the advent of iterative reconstruction algorithms it is now possible to add patient-specific attenuation maps into the reconstruction process, providing emission data sets that are fully compensated for photon attenuation. These patient-specific attenuation maps are created from a transmission scan of the patient. The camera acquires transmission projections in a similar way to its acquisition of emission projections, but with its energy window set to accept photons emitted from a transmission source located at the other side of the patient. Using a blank scan of the transmission source with no body between it and the camera, the photon flux emitted by the source is known. When the blank scan is compared to the transmission projections acquired with the patient in position, it is possible to ascertain the attenuation properties of the body. When these transmission projections are reconstructed a 3-D attenuation map of the patient is created. The additional radiation dose delivered to the patient from a transmission source is insignificant compared to the dose received from the injected radiopharmaceutical [3]. There are however other problems associated with the acquisition of transmission data sets. Transmission sources that are required to move, particularly if their movement is coordinated with electronic windowing, require careful engineering and additional quality control. If the transmission source does not provide an image of the whole width of the body, then truncation can occur causing artefacts in attenuation maps and subsequent problems in the reconstructed emission data sets. Consideration must also be given to crosstalk, the scattering of the higher energy photons (e.g. 140 keV photons from a 9 9 m T c radiopharmaceutical), into the energy window of the lower energy photons (e.g. 100 keV photons from a 1 5 3 Gd transmission source). This causes contamination of the transmission projections by the emission photons, or visa versa depending on the isotopes in use. The following is a list of possible transmission systems: • The most simple transmission source is a sheet source [4] (Figure 2.8a) which, while requiring no source motion and being very unlikely to cause truncation artefacts, is not the most practical method. Shielding and source handling are major considerations. • A line source at the central focus of fan beam collimator [5] (Figure 2.8b) allows a good compromise between spatial resolution and sensitivity for small regions of interest like the heart. This geometry also requires no source motion, and the source is relatively easy to handle. However, truncation and crosstalk need to be considered and the fan beam collimator must also be used for the emission Chapter 2: Background Information and Literature Review 17 acquisition which then requires fan beam reconstruction algorithms. A way round this problem is to use a multiple headed camera with a fan beam collimator for transmission imaging installed on one head, and parallel hole collimators for emission imaging installed on the additional heads [6]. Transmission and emission images are acquired sequentially, which introduces the problem of patient movement during or between scans. A solution to the truncation problem of the fan beam collimator is to use a fan beam collimator with an asymmetric focus [6] (Figure 2.8c). The truncation of only one side of the body can be compensated for by acquisition of projections from a full 360° rotation. Another solution to fan beam truncation is to use a parallel hole collimator and a higher energy transmission source [7] (Figure 2.8d). High energy photons penetrate through the lead structure of the collimator, allowing the transmission photons to be incident on the camera crystal. (a) camera and ^/'collimator (b) path of transmission photons i : i ^ i j # ,7 body of patient 'SSSS/SSSSSSSSSSSSSSSSSSSSS/SSS/S/S. (c) additional collimator transmission source (d) J • J • J • J Figure 2.8: Transmission source designs for 1 5 3 Gd, (a) collimated sheet source, (b) line source at central focus of fan beam collimator, and (c) line source with asymmetric fan beam collimator, (d) High energy Ba 1 3 3 line source with septal penetration of high energy photons through parallel beam collimator. Chapter 2: Background Information and Literature Review 18 The line source can be replaced by a moving point source, allowing easier shielding when not in use [8]. This method, in combination with a moving electronic window, allows for the reduction of crosstalk [8], however combining the electronics with the source motion is not simple. For all transmission source designs it has been suggested that both the transmission and emission projections can be used to reconstruct an improved attenuation map [9]. This method has been shown both to reduce noise and to provide a more uniform noise distribution. Another design of transmission source is the multiple line source system [10] (Figure 2.9a). This is the Profile transmission source fitted to the Siemens E-cam gamma camera. The source is 1 5 3 Gd which decays by electron capture, emitting y photons of 97 keV and 103 keV, with the peak emission profile at 100 keV [11]. This transmission source system was used for all the experiments carried out for this thesis. It shall therefore, now be discussed in more detail. (a) © © © © © x axis of graphs (b) and (c) (b) (c) position on source position on camera Figure 2.9: The Profile transmission system: (a) source design, (b) photon flux emitted by transmission source, and (c) photon flux reaching camera after being attenuated by the body. The design of the Profile system tailors the photon flux intensity to the shape of the body. It consists of collimated line sources placed opposite to the two camera heads, on which standard parallel hole collimators are installed. The sources lie parallel to the axis of rotation, with spacing and activity designed to produce a photon flux profile as close as possible to a smooth curve with the greatest activity in the centre (Figure 2.9b). Photons emitted at the centre of the system have to pass through the thickest part of the patient and will therefore be highly attenuated. Photons emitted at the edge of the source will pass through a thinner section of the body and will therefore experience less attenuation. The design of the source creates transmission projections with consistent signal-to-noise ratios across Chapter 2: Background Information and Literature Review 19 the whole projection (Figure 2.9c), and administers a smaller radiation dose to the patient than other transmission systems. The ratios in activity between the line sources are 0.3, 0.4, 0.55, 0.75, 1,1, 0.75, 0.55, 0.4, 0.3 which is an exponential relationship. Therefore, when the activity of the transmission source needs replenishing, each line source can be replaced by the line source of higher activity lying next to it and new sources are only required for the two central line sources [12]. This reduces the cost of replenishing the system. In the Profile system emission and transmission projections are acquired simultaneously and therefore transmission data sets (obtained from the lower energy photons) must be corrected for crosstalk. Transmission data sets are collected into three energy windows, a 20% energy window centred at 100 keV (7), an 8% window at 86 keV (S,) and a 12% window at 116 keV (S2). The crosstalk corrected transmission data sets (Tr) are calculated using the constant k = 1.1 defined from previous experiments [13]: T^T-kfa +S2) (2.3) The Profile transmission system was clinically validated with myocardial perfusion studies (number of clinical cases studied: N=171). The application of AC did not effect the sensitivity of the studies, but it did increase the specificity from 84% to 88% and the normalcy measured for patients with a low likelihood of CAD, from 78% to 85% [14]. Evaluations of current commercial AC techniques have shown that high quality attenuation maps are essential to emission image quality [15] [16]. Due to recent advances in software and hardware it is now possible to create attenuation maps from CT scans. The emission data sets and CT maps are either acquired on a dual modality system or acquired on separate systems and co-registered. CT maps have greater resolution and better signal-to-noise ratios than traditional maps and therefore may allow more accurate attenuation correction of emission data sets. Another advantage is the anatomical information provided by CT scans which can be used to put emission images in context [17]. However, CT scans deliver a higher radiation dose to the patient. CT scans were not available for the experiments carried out in this thesis. 2.3.2 Scatter correction The acceptance by the gamma camera of only photons with energies that fall within the 20% window around the photo-peak, cuts out many of the scattered photons. Problems caused by the scattered photons still accepted within this 20% window include poor image contrast, poor signal-to-noise ratios and an object-dependent distortion [18]. The following is a list of possible techniques to correct for these scattered photons: • Simple techniques include the use of a pre-reconstruction filter designed from the image response function of the degradation [19], or the use of broad beam attenuation coefficients during attenuation correction [20] [21]. Neither of these techniques provides satisfactory results. Chapter 2: Background Information and Literature Review 20 • The next subset of scatter correction (SC) techniques collects information from additional energy windows and uses this information to estimate the number of scattered photons being accepted in the energy window of the photo-peak. - The Compton window subtraction method [22], involves the use of a second energy window positioned just below the photo-peak window. The counts from this window are scaled and subtracted from the photo-peak counts. - The triple energy window method [23] [24], involves two narrow windows positioned at either side of the photo-peak. A linear interpolation between these windows provides an estimate of the scatter in the photo-peak window. - Other energy window based methods include the division of the photo-peak window into two sections and the relative height of each part used to estimate scatter [25] [26]; or the use of multiple energy windows [27] [28]. The main problem associated with these methods is that the photons accepted by these additional energy windows will have been scattered through different angles than the scattered photons accepted in the photo-peak window. The spatial distribution of this scatter estimate is therefore inaccurate. Another problem is the degradation of the signal-to-noise ratio in the photo-peak window. The 'corrected' photo-peak contains noise contributions from the subtracted energy windows in addition to its original noise. These methods also do not take into consideration photons that have undergone Rayleigh scattering and changed direction without losing energy. • The next set of SC techniques involve the measurement of the scatter point spread function (SPSF), this function describes the probability that a photon emitted from a particular voxel will undergo a scatter interaction and be detected by the camera. The SPSF is convolved with the original emission projections and the resultant scatter projections are subtracted from the original projections [29] [30] [31]. This method was also developed to incorporate the change in SPSF seen at varying distances from the camera [32] [33] [34] [35]. These methods show some good results, but as they involve the subtraction of scatter projections from original projections they still decrease the signal-to-noise ratio. • Due to increasing computational power it has recently become possible to base SC on the equations that govern scatter, including the Klein-Nishina formula for Compton scatter. Information derived from the activity distribution, the attenuation map and the theory of scatter can be used to correct for scatter within the iterative reconstruction process itself [36] [37] [38] [39] [40]. Some approximations are still required. - Monte Carlo simulations can be used calculate the probability density function that describes the propagation of individual photons through the scattering material. As only approximately 1 in every 10,000 photons will successfully travel through the collimator, processing time can be reduced by skewing the calculations to favour photons that are more likely to be successful [41] [42] [43] [44] [45]. Chapter 2: Background Information and Literature Review 21 - The ultimate method of SC is the analytical calculation of scatter [46]. Again the computational demand is high but it is possible to reduce the time involved by pre-calculating a look-up table specific to the collimator and projection angles. An example of this, the analytical photon distribution (APD) scatter correction method [47], has recently been developed into the APD interpolation (APDI) method [18] to significantly reduce its processing time. The result is an accurate method, ideal for use in clinical research. This SC technique was used for all the experiments carried out for this thesis. It shall therefore now be discussed in more detail. Both the APD and APDI methods calculate the distributions of primary (unscattered) photons, first and second order Compton scattered photons (that have scattered once or twice in their path through the body) [48], and first order Rayleigh scattered photons [49]. Approximations for higher order Compton scatter are also included. The APD method calculates the SPSF using the 3-D integrals of the equations that account for photon absorption, Compton scatter and Rayleigh scatter; the density of electrons in the medium (derived from the attenuation map); and the detection of photons by the camera. The majority of these parameters can be pre-calculated and introduced as a look-up table. Once calculated for each voxel, the SPSF's are multiplied by the activity for that voxel (derived from a reconstruction of the emission data set), and the results are summed over all voxels containing activity to give the total scatter distribution function. This is the distribution of scattered photons in the activity map. The APDI method [18] calculates the SPSF as above, but for a much smaller number of voxels arranged in an evenly-spaced grid (one every four voxels in each dimension, and only in voxels that contain activity). A tri-linear interpolation is then used to estimate the SPSFs of the remaining voxels. The distribution of scatter photons within the activity map is calculated as before. This interpolation is a valid approximation because the spatial characteristics of scatter vary slowly. Both the APD and the APDI methods have been thoroughly tested using computer simulations and physical phantoms. 2.3.3 Detector response compensation Distance-dependent resolution loss caused by the camera's collimator means that measurements of volume, distance or counts, taken at different positions within a reconstructed data set are not directly comparable. The following is a list of possible detector response compensation (DRC) techniques: • Pre-reconstruction filters can be used to help restore the resolution of an image, these are usually the Metz or Wiener filters [50]. The filter design can be optimised using a priori knowledge of the system, or using frequency information from the emission projections [51]. However, these filters decrease the signal-to-noise ratios and occasionally result in circular noise artefacts [52]. • More advanced techniques for DRC are based on the geometric point spread function (GPSF) of the imaging system and are applied during iterative reconstruction [53]. These methods do not decrease the signal-to-noise ratio of projections [54]. Chapter 2: Background Information and Literature Review 22 - Computational demand can be reduced by calculating DRC slab-by-slab rather than slice-by-slice, where a slab is a number of neighbouring slices [55], or by approximating the GPSF and blurring it incrementally with distance [56]. - Comprehensive corrections use a 3-D GPSF modelled from a depth-dependent Gaussian function with a full-width at half-maximum (FWHM) proportional to the resolution of the system. This 3-D method corrects for distance-dependent resolution loss between slices in addition to corrections within each slice. The method has been shown to improve the signal-to-noise ratio in addition to improving spatial resolution [57]. This DRC technique was used for all the experiments carried out for this thesis. It shall therefore, now be discussed in more detail. The spatial resolution of the system (camera including collimator, Rsystem), is defined as the FWHM of the image of a point source at distance d from the collimator face. This FWHM is a dependent on the intrinsic resolution of the crystal (R,„,) and the resolution of the collimator at that distance d from the collimator (Rcou). The relationship between these parameters is as follows: R system = ^ Kol^ + ^inf 2 ( 2 - 1 ) The Rcon can be defined from the geometric parameters of the distance between the collimator and the point source (d), the collimator's thickness (h), the diameter of its holes (e), and the distance between the crystal and the collimator (b): Rcou ={(d + h + b) (2.2) h This can be rearranged to form the following equation: Rcoi, = <*\d + a2 (2.3) with o,=— and a2 =—(h + b)& s assuming b « h h h It is therefore possible to calculate R s y s t e m at any distance from the collimator (d), knowing only the intrinsic resolution of the crystal (Rint), the collimator's thickness (h) and the diameter of its holes (e). These parameters are used in modelling the 3-D GPSF for the DRC method. 2.3.4 Incorporating corrections in SPECT reconstruction The processes involved in the acquisition of SPECT projections and the reconstruction of these projections to form a 3-D data set can be described by simple equations. The formation of SPECT projections Y , from an activity distribution X , is described by the following equation: Y = Cl (2.4) The matrix C is the system matrix and it describes the probability that a photon emitted at a particular point in the object will be accepted by a specific pixel in a particular projection. The reconstruction of Chapter 2: Background Information and Literature Review 23 SPECT projections to form an image data set Xtsttmalt, that is an estimate of the original activity distribution, initially appears to be a simple matter of inversing equation 2.4: Kstimale = C (2.5) However, matrix C is very large and unless it contains many zeros, its inverse is impossible to calculate. A matrix that includes the influence of scatter through the body will not contain many zeros. Another method is therefore required. 2.3.4.1 Filtered back-projection The simplest method of reconstruction is the analytical calculation of back-projection. Here the projections taken from the object are back-projected onto an image matrix (Figure 2.10). Essentially the number of photons recorded in each projection pixel is spread back along the line (perpendicular to the camera face) from which the photons originally came. When this process is performed for every acquired projection, the lines of potential source positions intersect and reinforce each other, indicating the true location of the source. Each reconstructed source will have a 'star'-like appearance until a sufficient number of projections have been back-projected (Figure 2.10b). The image will also appeared blurred. This anomaly is partially corrected for by convolving the image with the sine function, artificially decreasing the counts reconstructed around each object [58]. (a) Acquisition of two projections Amplitude of projection Body with hot tumor Camera (b) Two projections back-projected onto an image matrix 7 Back-projected image Figure 2.10: The process of filtered back-projection in 2-D. A more accurate but still analytically simple technique is that of filter back-projection (FBP). Each projection or reconstructed image can be described in the spatial frequency domain through the Chapter 2: Background Information and Literature Review 24 application of a Fourier transform. A convolution with a sine functionin the spatial domain becomes a multiplication with a ramp filter \k\ in the spatial frequency domain. This is a less computationally demanding task, particularly as it can be performed on the projection data set before reconstruction. However, a multiplication with a ramp filter will amplify signals from the higher frequencies associated only with noise and not with image detail. A second (apodising) filter is therefore required to dampen these high frequency signals [59]. The process of FBP involves the multiplication of the Fourier transform of each projection with both the ramp and apodising filters. An inverse Fourier transform is then applied to each projection to return it to the spatial domain, and these altered projections are back-projected as described above. If no noise is present in the original projections, FBP can produce an exact image of the object. However, noise is always present in nuclear medicine projections. FBP is the most common method of SPECT reconstruction as it is fast and less computationally demanding than iterative algorithms. However there are many problems associated with its use. The apodising filter used to decrease image noise also causes a loss in spatial resolution, and for source objects containing a significantly greater activity than the surrounding background, the blurring artefact is only partially corrected by the ramp filter. However, the most significant problem is that FBP cannot incorporate modelling for AC, SC, DRC or statistical noise [60]. It is therefore necessary to look at iterative algorithms for comprehensive SPECT reconstruction. 2.3.4.1 Iterative reconstruction algorithms In an iterative algorithm a guess X s is made as to the original activity distribution, which can be multiplied by the system matrix to produce a guess of the projections CX . This is known as a forward-projection. These new projections can be compared to the measured projections using an iterative algorithm, which successively provides guesses of activity distribution that are closer to the truth. Within this iterative structure other information can be included, such as estimates of scatter projections, the patient-specific attenuation map, and a model of the GPSF. Regularizers can also be included that enforce a priori knowledge of the activity distribution, e.g. knowledge of the smoothness of activity changes within the body, or the Poisson distribution of the count statistics in the projections. Several iterative algorithms can be used, and the most common is the maximum likelihood expectation maximization (MLEM), which implicitly assumes Poisson distributed statistical noise in the projections. The basic format of this algorithm can be summarized in the following word equation using n as the number of iterations and 'image' as the activity distribution estimate [60]: imagen+1 = image" x normalized back-projection of (original projections/projections of image") (2.6) Chapter 6: Results and Discussion 25 Mathematically the MLEM algorithm is described in the following equation: A"  N C Y ^--P-I.-TP— 1=1 k=\ Where is the estimate of activity in voxel j after the n'h iteration, Y, is the number of counts recorded in projection pixel /, and Qj is the system matrix element for those values of / and / N is the number of projection pixels. The denominator of the summed term is the forward-projection, a calculation of the estimated value of projection pixel /' summed over M, all voxels in the reconstructed object. To speed up calculations block iterative methods are used [61] [62] [63]. Instead of each iteration being defined as one calculation involving all acquired projections; a block iteration is a number of calculations each carried out using a different subset of projections. The image estimate is updated after each subset calculation, and is therefore updated several times during a complete block iteration. A good estimate of the original activity distribution can be reached using a smaller number of iterations. Ordered subset expectation maximization (OSEM) is the block iterative method applied to the MLEM algorithm [64]. Corrections for photon attenuation, photon scatter and/or distance-dependent resolution loss have been added to iterative algorithms [65] [66] [67] [68] [34]. The inclusion of AC, SC and DRC has been shown to improve signal-to-noise ratios, object size, shape recognition, and quantitative activity concentration ratios [69]. To speed up algorithms that involve SC, it is possible to include this correction in the forward-projection term only and not in the back-projection term. This results in unmatched forward/back-projector pairs [70] [71] [53]. It is also possible to calculate photon scatter on the first few iterations and then keep it constant, or to only update photon scatter every few iterations [36]. DRC can also be added into the forward-projection term only [53] [71]. For all the experiments carried out in this thesis, the OSEM algorithm incorporates the attenuation map produced by the Profile transmission system [10], the APDI scatter correction method [18], and the 3-D GPSF modelled from a depth-dependent Gaussian function [57]. DRC and AC are incorporated within the system matrix in both the forward-projection step (denominator of the summed term) and back-projection step (numerator of the summed term). SC is included in only the forward-projection step and as a separate term: 2" C V V - 4h-1-5 — — P-» *=I j=\ In comparison to equation 2.7, equation 2.8 shows the estimate of activity in voxel j after the nm iteration to be summed over Sn, the ordered subset of projection angles for iteration n. The APDI term is 25 Chapter 2: Background Information and Literature Review 26 the summation over all voxels of the interpolated SPFS multiplied by A. , the initial estimate of activity in voxel j, derived from an OSEM reconstruction of the original projections but incorporating only DRC and broad beam AC. Chapter 2: Background Information and Literature Review 27 2.4 Clinical situations in which quantitative accuracy is important The diagnostic value of nuclear medicine studies is related both to the accuracy of the resultant data set, and to the subject under investigation. If quantitative information is required from the study, then very accurate images are essential to provide the diagnostic information required. This thesis investigates the most demanding of diagnostic tasks: the measurement of radiation dose absorbed by a tumor; the absolute thickness of the myocardial wall; and the relative size of a myocardial perfusion infarct. Quantitative accuracy is of utmost importance in these fields of dosimetry and myocardial perfusion, and this work determines the importance of AC, SC and DRC in producing the accurate quantitative information required. This section describes the clinical importance of dosimetry and myocardial perfusion, and details the specific diagnostic problems associated with photon attenuation, photon scatter and distance-dependent resolution loss. 2.4.1 Dosimetry 2.4.1.1 The clinical importance of dosimetry Nuclear medicine involves the injection of radioactive compounds into a patient's body. However, the energy deposited by radiation in the body can cause damage to living tissue and therefore must be monitored. The amount of energy absorbed by a unit mass of tissue from ionising radiation is called the radiation dose, and the measurement of that dose is dosimetry. Ionising radiation may originate from sources inside or outside the body, leading to the measurement of internal and external dose, respectively. In nuclear medicine the radioactive source of interest is inside the body and therefore all references to dose and dosimetry in this thesis, will be references to internal dose and internal dosimetry. For diagnostic purposes the radioactive tracer is administered to enable imaging, and therefore tissue damage is an undesirable effect. Consequentially, before any radiopharmaceutical is approved for routine clinical use, multiple dosimetry studies must be performed. These studies ensure that the activity of tracer required to provide clear images, will not damage any tissue by administering a significant radiation dose to it. For women, particular note is taken of the dose received by the uterus. This is used to calculate the dose that would be administered to a foetus, if present. Depending on the stage of development, a very small radiation dose can have a significant effect on a foetus. Nuclear medicine can also be used for therapeutic purposes. In this case the radioactive compound is designed to kill diseased tissue. The activity of a therapeutic administration must therefore be carefully chosen to provide a lethal dose to the diseased tissue, without harming healthy tissue, particularly that of very sensitive or critical organs. As the relationship between the dose administered to the diseased tissue and that administered to the surrounding tissue is now of critical importance, dosimetry plays an essential role in the development of new therapeutic radiopharmaceuticals. In the case of many therapeutic compounds now in routine clinical use, the uptake of the compound is highly Chapter 2: Background Information and Literature Review 28 dependent on the patient. It is therefore necessary to carry out a dosimetry study on each individual patient to determine an effective course of treatment. Dose can be caused by radiation emitted from any organ that takes up the radiopharmaceutical, whether it is absorbed by that organ or any other organ in the proximity (Figure 2.11). The distribution of activity within the body is therefore of particular importance to the calculation of dose. This distribution of activity is known as the biodistribution and is measured from a nuclear medicine imaging scan. Most therapeutic radiopharmaceuticals emit p or a particles only and are therefore not suitable for imaging with a gamma camera. Therefore if information on the biodistribution of a therapeutic radiopharmaceutical is required, a y emitting radiopharmaceutical with similar properties is used in its place. Information required for dosimetry in addition to biodistribution, includes the physical decay ofthe radionuclide [72] [73] [74], the administered activity and the biological half-live of the radiopharmaceutical [75]. Figure 2.11: Dosimetry involves the measurement of radiation dose to each organ from radiation emitted by the organs that take up the radiopharmaceutical. In this particular example a radiopharmaceutical designed to image the liver is also taken up by the lungs. The dose to the lungs will depend upon the amount of radiation emitted in both the lungs and the liver, the dose to the liver will depend upon the amount of radiation emitted in the liver and the lungs. Also important is the dose to the kidneys which lie close to the liver and are very sensitive to radiation, these are the critical organs for this particular test. 2.4.1.2 Radioimmunotherapy - a specific clinical example Each field of nuclear medicine, whether therapeutic or diagnostic, has similar needs for dosimetry to accurately determine the radiation dose administered to each organ. However, to appreciate the need for accurate radiation dosimetry, it is necessary to look at a particular example. Radioimmunotherapy (RIT) is a technique which utilizes the ablative properties of radiation by delivering radioactive particles directly to the tumor cells. The routinely used immunotherapy involves the introduction of a monoclonal 51 - Target D - Critical • - Other Chapter 2: Background Information and Literature Review 29 antibody (MAb) to the patient. The MAb is chosen to correlate to the antigen expressed on the tumor cells known to be present. The antibody is engineered either to have a direct cytotoxic effect on these tumor cells or to induce the host's immune effecter mechanisms [76]. RIT adds a twist to the theory of immunotherapy. The MAb molecules are labelled with a radioactive isotope that emits p-particles. Most of these p-particles will be absorbed within a few millimetres of the tumour cell resulting in a radiation dose to the tumor additional to the cytotoxic effects of the MAb itself. Due to the limited range of p-particles this radiation does not significantly penetrate into the healthy tissue cells beyond the tumor [76]. An example of RIT is the 9 0 Y labelled antibody to CD20 now routinely used to treat B-cell non-Hodgkin Lymphoma [77]. The 1 1 1ln labelled antibody to CD20 is used as a substitute isotope for biodistribution imaging [78] [79] and therefore to determine the dosimetry of 9 0 Y. Research into RIT is prolific and includes topics such as the appropriate choice of radionuclide [80] and monoclonal antibody [81] [82] to produce new RIT products; timing the administrations to give maximum dose to the tumor and minimum dose to the critical organ(s) [83]; techniques available to increase the effect that the absorbed dose has on the tumor; and comparison of existing products to find the most efficient [84]. Although individual dosimetry is not required for treatment of non-Hodgkin Lymphoma with Y 9 0 labelled anti-CD20 MAb [85] [86], when a new RIT product is introduced, dosimetry is required to tailor each individual dose to each patient. Another essential role of dosimetry in the field of RIT is the calculation of dose administered to bone marrow. This is the critical organ associated with RIT. 9 0 Y has a high affinity for bone if it is separated from its MAb [87]. Radiation damage to the bone marrow results in haemotoxicity which can prove fatal. Bone marrow transplants have been used on several occasions to counteract this phenomenon but this procedure is not only invasive but requires a matched human donor. The prevention of haemotoxicity or its limitation to a tolerable level is the major factor that limits the activity that can be administered during RIT. Research is continuing in this area, requiring accurate dosimetry [88] [89]. Due to the difficulty in measuring the biodistribution of activity within the bone marrow from planar images, research is also investigating the estimation of bone marrow dose from blood dose [90], or from imaging the sacrum (base ofthe spine) known to contain 9.9% [91] ofthe body's total red bone marrow [87]. 2.4.1.3 Internal dosimetry calculations The Medical Internal Radiation Dose Committee of the Society of Nuclear Medicine (MIRD) was created in 1969 to lay down guidelines to allow the accurate estimation of dose to individual organs and the whole body. These guidelines are still used today. In the following discussion the organ for which dosimetry is being calculated shall be referred to as the target organ, and any organ that shows uptake of the radiopharmaceutical exceeding the average concentration in the body shall be referred to as a source organ. Chapter 2: Background Information and Literature Review 30 The mathematical definition of the radiation absorbed dose D = , the energy AE deposited by Am ionising radiation in a mass Am. The amount of energy deposited (absorbed) is a function of the energy released per decay and the number of decays within the region. It also depends on the type of radioactive decay, and its penetration properties. Essentially it is the energy incident upon or released in the target region, multiplied by the fraction that is absorbed by that region. Therefore the MIRD definition of mean absorbed dose to the target region rk from a uniformly distributed activity in the source region rh is [92]: D\ rk ^  rh) = TZ (2.9) Where Ah is the cumulated activity in source region rh (i.e. the total number of decays that occur during the total time the radiopharmaceutical is present in the source organ); Mk is the mass of the target region; A, is the average energy emitted per nuclear decay in the form of radiation /', also known as the radionuclide specific equilibrium dose constant for radiation type ;'; and^.fo <— rh) is the absorbed fraction in rk of radiation /' emitted in rh. The product of the last two terms is therefore summed over all types of radiation. The parameterOt(rk <— rh) is the specific <p, i.e. the absorbed fraction in rk of radiation / emitted in rh per unit mass of rk: 6. Equation 2.9 can also be summarized as: D{rk +-rh) = AhS(rk <-rh) (2.11) Where the S factor is specific for each source/target combination for the radionuclide of interest. So to sum over all the observed dose contributions from all n source regions: ^ t ) = l [ i 4 < - r j ] (2.12) n The S factor is defined as the absorbed dose per unit of cumulated activity and is therefore dependent on the penetration of the radiation in question. Values of S are calculated by MIRD and tabulated for different isotopes [93]. Calculations are simple for non-penetrating radiation such as p, a, conversion e", X and y with energies below 11keV, all of which will have a penetration depth of less than 1cm in tissue. For penetrating radiations such as X and y with energies above 11keV, S factor calculation includes Monte Carlo simulations based on the original 70kg 'standard man' model [91]. There are also special case calculations derived from models of a newborn, a 1 year old, a 5 year old, a 10 year old, a 15 year old, an adult female and pregnant females at 3, 6 and 9 months gestation. Chapter 2: Background Information and Literature Review 31 Obviously real patients will differ greatly from standard models, particularly those with disease as all models are based on healthy individuals and tumour geometries are not normal source organs. MIRD S factors are unsuitable for monoclonal antibodies (a type of radiopharmaceutical which was developed subsequent to the calculation of the majority of S factors), which are designed to target antibodies associated with malignant cells and as such are not localized in specific volumes. S factors also do not take into account the dose absorbed by the background tissue from the source organ, or that absorbed by the target organ from the background tissue. Monte Carlo based software programs are now available that begin to redress these problems. The software requires an anatomical map of each patient which can be provided from a CT or MRI study [94]. The only parameter now missing from equation 2.12 is the cumulated activity Ah. The reduction in activity over time in a source region is: A(t) = A0e'^' (2.13) Where the effective decay constant Aeff, is derived from the physical and biological half-lives of the radiopharmaceutical (Tp and Tb respectively): 1 1 1 In 2 = -— + — and Ty2 = ••Kff=^P+^ (2-14) As Tb is an unknown quantity, a time/activity curve A(t) must be formed by measuring the activity in the region of interest over time. Cumulated activity is then an integration of this time/activity curve between the injection time (f=0) and infinity: r Jo To form a time/activity curve it is necessary to measure the biodistribution of activity within the body at a number of time intervals after the administration of activity. It is standard practice to acquire planar images from which to measure biodistribution. Anterior and posterior images are required, as is a calibration scan. In its simplest form the biodistribution from planar acquisitions can be calculated using arithmetic or geometric means (PAri and PGeo, respectively) of the intensities of the anterior and posterior images (lA and lP, respectively): A = [Ah(t)dt (2.15) V ^ J PGeo = -J^A-h) E X P 2 (2.16) (2.17) Where L is the measured maximum patient thickness, and p is the linear attenuation coefficient for water at the energy of the photons in question. The linear attenuation coefficient for water is used as it is easy to measure experimentally, and the density of water is similar to that of soft tissue. Chapter 2: Background Information and Literature Review 32 Scans are normally taken immediately post-injection and repeated at time intervals thereafter until (for therapeutic dosimetry) the activity has decreased to 10% of the initial measurement. The activity in each organ can then be plotted over time, and a mathematical curve found to fit the data. The curve is integrated from time zero to infinity to find the total cumulative activity Ah as in equation 2.15. The mean absorbed dose D(rk) to the target organ can then be calculated from the MIRD tables of S factors and equation 2.12. Although planar dosimetry is good enough to give an indication of organ doses in simple situations [95], it is by no means accurate enough for more complex conditions. As the body is only viewed from the anterior and posterior directions, problems include organ overlap. This occurs where two organs overlie each other in the image making it impossible to resolve each organ separately and hence to draw the required time/activity curves. Another limitation is the lack of information obtained on the distribution of activity within the organ, which in many cases is not uniform [96], However, the most significant problem in the use of planar dosimetry is the application of a single factor to correct for photon attenuation throughout the entire body. This factor is calculated from the maximum thickness of the body and hence overestimates the attenuation of photons originating in the thinner regions of the patient (the lateral edges of the patient in an anterior or posterior scan). This leads to an overestimation of counts from these regions. The use of a single linear attenuation coefficient assumes that all tissues are of a similar density. However, the attenuation properties of the body are not uniform, with, regions such as lung, dense muscle and bone displaying significantly different properties. The planar dosimetry methods described by MIRD were originally designed for diagnostic and not therapeutic studies, and because of that general assumptions were made for ease of calculations [97]. However, some recent clinical trials that involve dose calculations of therapeutic radiopharmaceuticals, still base their dosimetry on planar acquisitions. These include trials that investigate the dosimetry for 9 0 Y therapy [98] [99] [100] [101] [102] [103]. 2.4.1.4 The effect of SPECT corrections on the accuracy of dosimetry As the use of planar projections to measure the biodistribution of activity is an estimation at best, the use of SPECT studies will provide a noticeable improvement to the accuracy of dosimetry. With the improved 3-D resolution of SPECT data sets over planar images, it is possible to differentiate between organs lying close to each other, and to depict non standard tumor geometries. Better resolution also offers the potential to split up the tumor or organ volume to account for inhomogeneous activity distributions. Several clinical studies have looked at the effect of deriving biodistributions from SPECT data sets. In these studies data sets reconstructed even with no corrections or only very simple corrections, were found to provide dosimetry results significantly more accurate than those derived from planar acquisitions [104] [105] [106]. The accuracy of dosimetry will be further improved by the use of patient-specific AC, SC and DRC methods during the reconstruction of SPECT data sets. It should be noted that accurate corrections are not simple to apply and the computational power required and therefore time involved may prove Chapter 2: Background Information and Literature Review 33 prohibitive. Previous studies have looked at the effect of deriving biodistributions from SPECT data sets reconstructed using various corrections. Corrections for AC and SC derived from CT density maps were found to enhance the accuracy of biodistribution estimates for computer simulations [107]. An 1 1 1ln phantom study showed patient-specific AC from nuclear medicine transmission scans to increase image quality, increase quantitative accuracy and decreased noise [108]. An 1 2 3 l phantom study found that patient-specific AC produces more accurate biodistribution estimates than the Chang method of AC, and that dual-window SC provides better results than the use of broad beam attenuation coefficients in AC [109]. An 1311 phantom study and clinical data showed the dual-window SC to produce biodistribution estimates that correlate well with the measurement of blood samples (R=0.955) [110]. As no dosimetry studies have been carried out using DRC modelled from a depth-dependent Gaussian function, or the APD/APDI method of SC, this thesis tests their ability (together with patient-specific AC) to accurately determine tumour activity. 2.4.2 Myocardial perfusion 2.4.2.1 The clinical importance of myocardial perfusion imaging SPECT is routinely used for the evaluation of patients with suspected coronary artery disease (CAD) [111]. CAD is a condition that causes the blockage of arteries that feed the myocardium (the heart muscle). If the blood flow (perfusion) to a section of the myocardium is reduced then the function of that section is also reduced. The tissue in this section may remain viable, this means that if the perfusion is restored, the myocardium will eventually function normally. This case is known as reversible ischemia. However, if the reduction in perfusion is prolonged or severe, the damage done to the myocardium may be irreversible. In this case the tissue is no longer viable and is infarcted. By studying the perfusion of the myocardium when the patient is at rest and again after exercise (stress), clinicians can distinguish between healthy tissue, reversible ischemia and infarcted myocardium. It has been shown that the results of myocardial perfusion studies correlate well with patient prognosis [112] and the detection of CAD [113]. Originally 201TI was used as the isotope of choice for myocardial perfusion imaging, but as 9 9 m T c has shorter radioactive half-life than 201TI, much higher activities can be administered. Additionally the higher energy of the y-radiation emitted by 9 9 m T c results in less attenuation of photons as they travel through the body. Both these factors result in the improved image quality of 9 9 m T c over 201TI. The most common radiopharmaceutical used presently for myocardial perfusion studies is technetium-99m-hexakis-2-methoxyisobutyl isonitrile, more commonly known as 99mTc-Sestimibi [114]. 99mTc-Sestimibi is passively transported across plasma and mitochondrial membranes, and is held within the mitochondrial matrix by large negative trans-membrane potentials. If the mitochondrial membrane is injured and therefore depolarised, then uptake and cellular retention is impaired [115]. The distribution of 99mTc-Sestimibi is thus dependent on myocardial perfusion and viability. Chapter 2: Background Information and Literature Review 34 The disadvantage of aamTc-Sestimibi is excessive isotope uptake in the liver, gall bladder, small and large bowel, or stomach, all of which lie close to or overlying the myocardium and therefore cause artefacts in the image of the myocardium. Isotope uptake in the liver, gall bladder and bowel is due to the excretion of 99mTc-Sestimibi by the hepatobiliary system. Stomach uptake results from any subsequent duodeno-gastric reflux [116]. All hepatic activity is increased when pharmacological agents are used to stress the patient to simulate exercise. The usual manifestation of this problem is an alteration in counts recorded from the inferior wall of the left ventricle (LV) [117] [118] [119] which means that the true counts in this area cannot be ascertained thus negating any diagnosis of the region. This alteration in counts is caused by several factors: the attenuation of photons in the dense tissue of the liver; the poor and asymmetric resolution at this depth resulting from the geometry of the collimator; and the capability of photons originating in the area of the liver, to scatter in the tissue of the myocardium and hence to appear to come from that region. Imaging centres use a variety of measures to mitigate the problem of hepatic activity: a meal to increase stomach volume [120], low level exercise to reduce liver blood flow [121] [122], imaging the patient lying on their front [123], or waiting for the hepatic activity to dissipate [116]. However, as these methods increase patient discomfort and clinical time, clinicians are often required to report from myocardial perfusion studies with significant hepatic uptake. In addition to the interference of hepatic activity with the visualization of the inferior myocardial wall, decreased uptake in the anterior and inferior walls of women and men respectively, is often seen, irrespective of hepatic uptake [124]. The decreased uptake seen in the anterior wall of many female patients is due to the additional attenuation of photons as they pass through the dense tissue of the breast. The decreased uptake seen in the inferior wall of male (and sometimes female) patients is due to photon attenuation in the developed diaphragm muscle. 2.4.2.2 The clinical importance of myocardial wall thickness The myocardium is one of the most difficult organs in the body to image accurately. It displays a complex geometry and not only beats throughout the acquisition process, but is also effected by respiratory movement (breathing). It is positioned deep inside the body which results in large photon attenuation and resolution loss. For an accurate assessment of this organ it is therefore necessary to define a parameter that can assess the absolute quantitation of the entire (global) myocardium. Myocardial wall thickness can be measured at numerous positions around the LV, with a mean value of these measurements providing a global indication of wall thickness. The presence of the image artefacts discussed in the previous section will distort the apparent thickness of the affected myocardial walls. Any attempt to correct for these artefacts will be reflected in a change in myocardial wall thickness. Chapter 2: Background Information and Literature Review 35 An additional advantage of this parameter is that its average value is known for clinical data. Although the wall thickness of an individual patient will not be known without additional tests being performed, the average end-systolic (contracted) and end-diastolic (relaxed) thickness of male and female patients have been measured using MRI and 2-D echocardiography studies [125] [126] [127]. It is therefore possible to determine if the average wall thickness of a group of patients lies closer too or further from the probable true wall thickness. For these reasons, myocardial wall thickness is used in this thesis as one of the two indicators of myocardial quantitation. It is the only parameter measured in this thesis where the results obtained from clinical studies can be compared to the probable truth. 2.4.2.3 The clinical importance of myocardial perfusion infarct size Standard myocardial perfusion study clinical reports provide only an estimate of the size of any perfusion defect [128]. A defect encompassing less than 10% of the entire myocardium is reported as small, a defect between 10% and 20% is reported as medium, a defect greater than 20% is large and a defect greater than 40% is probably not survivable. However, there are situations when an exact measurement of the size of a perfusion defect is essential. These are mainly research situations and include the assessment of new and different treatment methods, such as for example the comparison of cardiac catheters. Originally, early mortality (30 days post treatment) was used as an endpoint to evaluate new therapies. However existing therapies are now so good that a huge patient cohort would be required to show a significant improvement in early mortality with a new therapy. Precise infarct size measurement is now being used as a surrogate end point to indicate late mortality (5 to 10 years post therapy), therefore requiring a smaller patient cohort [129]. The use of myocardial infarct size to indicate late mortality was initiated by clinical trials. These trials demonstrated the ability of myocardial infarct size to predict the survival of patients with CAD [130], to show good correlation with mortality at 2 years post therapy [131], and to show good correlation with pathological fibrosis in the human heart [132]. To date many studies have been carried out using infarct size as an end point to investigate the outcome of new treatment regimes, some have shown positive results [133] [134] [135] [136] and some not [134] [137] [138]. Myocardial infarct size can also be used to investigate the relationship between 99mTc-Sestimibi distribution and the severity of arterial blockage (assessed using angiography), or the risk to the patient from arterial blockage (assessed by measuring arteriole pressures). The accurate measurement of myocardial infarct size is severely limited by the distorting effects of artefacts present in the original images. The correction of these artefacts will result in a more accurate determination of infarct size. In addition, myocardial infarct size is a relative measurement; the measurement of one parameter compared to another, in this case the volume of the infarct divided by the volume of the complete LV myocardium. For these reasons and for the significant diagnostic value Chapter 2: Background Information and Literature Review 36 of its accurate determination, myocardial perfusion infarct size is used in this thesis as the second ofthe two indicators of myocardial quantitation. 2.4.2.4 Reorientation ofthe heart Due to the orientation of the heart in the thorax, conventional image slices of the body (transverse, sagittal and coronal) are not suitable to view the myocardium to its best advantage. The conventional system for viewing myocardial images is therefore based on a coordinate system centred around the central axis of the LV, producing short axis, horizontal long axis and vertical long axis slices, see Figure 2.12 [139]. The process of moving a data set from its original coordinate system to this cardiac orientation as known as reorientation, and involves a mathematical interpolation of the data set. Horizontal Long Axis Apex Septal Lateral Short Axis Septal Base Anterior Lateral Inferior Vertical Long Axis Anterior Base Apex Inferior Slices viewed from Inferior ->• Anterior Slices viewed from Base -» Apex Slices viewed from Septal -» Lateral Right ventricle Left ventricle Figure 2.12: Presentation ofthe myocardium ofthe left ventricle after reorientation. Chapter 2: Background Information and Literature Review 37 2.4.2.5 Methods used for the evaluation of myocardial defect size An additional barrier to the accurate measurement of myocardial infarct size is the methodology used to accomplish the measurement. Most methods of measuring the size and severity of myocardial defects rely on the creation of a polar map. This is a method of visualizing the 3-D volume of the LV on a 2-D map. To form the polar map a circumferential count profile is created from each short axis slice (Figure 2.13). These profiles are then plotted onto the concentric rings of the map, with the apical slice in the centre and basal slice outermost. Each polar map is created from an equal numbers of samples and is therefore identical in size to all other polar maps regardless of the size of the original hearts. Polar maps, the standard representation of the 3-D myocardium, can therefore easily be used to compare different clinical cases [140]. However, a polar map is only an approximation of the 3-D LV. As each concentric ring has a different area, the counts in each circumferential count profile must be rescaled to correct for the area difference. This causes a 'fish-eye' distortion of polar maps which results in defects at the apex appearing smaller and defects at the base appearing larger than their true size [141]. As an equal number of samples is taken from each heart to allow for inter-heart comparisons, large hearts will be under-sampled. Additionally, a circumferential count profile does not sample the entire width of the myocardial wall. This means that small defects or edges of larger defects that do not extend the entire width of the wall, may be ignored. Figure 2.13: (a) Definition of short axis slice through LV myocardium used to (b) create circumferential profile plotted onto polar map. Chapter 2: Background Information and Literature Review 38 Many software packages are available that measure the size and severity of myocardial defects. Most rely on similar methodologies based on the comparison of the investigated polar map to a database made up of 'normal' clinical cases. In the creation of this database, hearts are considered 'normal' if they are known to have a less than 5% likelihood of CAD. The following is a list of myocardial perfusion software packages: • The method pioneered at the Mayo Clinic was originally based on only three, representative short axis slices of the LV, subsequent versions of the method use five slices. Each of these slices is used to produce a maximum count circumferential profile (the maximum count in each 6 degree radial segment). The fraction of each profile that falls below 60% of maximum in that slice, is defined as a defect. Using a thorax phantom with solid and therefore inactive inserts to simulate myocardial defects, the method was found to provide measurements with a good correlation with the truth (R2=0.996) [142]. The use of a reconstruction technique that includes a correction for photon scatter requires the 60% threshold defining the size of the defect, to be reduced to 55% [143]. The major advantage of this method is that it does not require a comparison with a normal heart database, nor does it require the determination of the myocardial wall thickness. It does however rely on the assumption that the LV has a uniform thickness which has been shown clinically to not be true, leading to differing sensitivity in different defect locations. In addition the sampling is incomplete as only one maximum value is taken from each section of the heart wall. This means that defects not involving the entire thickness of the wall (sub-endocardial defects), are not detected. Additionally, the use of only a sample of slices results in problems detecting and measuring defects in the apex of the LV [142]. The present version of the Mayo Clinic software has been used in many clinical trials [144] [145] [134], including the EMERALD trial [146] [147]. • 4D-MSPECT is the myocardial perfusion quantification software from the University of Michigan [148] [149]. The endocardial and epicardial surfaces (the internal and external surfaces of the myocardium) are automatically rendered using splines to estimate the curvature of any missing sections. The myocardial activity is sampled from the midpoint between these surfaces (the mid-myocardial surface) and used to create a polar map which is compared to a normal heart database. The creation of each normal heart database requires 30 patients with a low-likelihood of CAD, with separate databases required for males and females for each radiopharmaceutical in use. The counts of each pixel in the investigated polar map are compared against the corresponding pixel in the database. The pixel is classified as a defect if its counts fall more than 2.5 standard deviations below the mean value of the database. The severity of each defect is categorized using a scale based on the number of standard deviations it falls below the mean value of the database [150]. Like many other software packages 4D-MSPECT includes the ability to measure the left ventricle ejection fraction (LVEF, the fraction of blood present in the LV which is ejected in each heart beat), and the LV volume at different phases in the cardiac cycle [151]. The software also includes an integrated reporting system which saves time for the attending physicians [152], The method Chapter 2: Background Information and Literature Review 39 compares favourably to the CEqual software detailed below [150], and correlates with the measurement of other physiological indicators, e.g. total peak creatine kinase enzyme release (R=0.64) [153]. Several clinical trials have been performed using 4D-MSPECT [154] [155] [156] [140]. • The CEqual software developed by Cedars-Sinai Medical Centre and Emory University uses maximum circumferential count profiles (as per the Mayo Clinic method) derived from each short axis slice to create a polar map. This polar map is then compared to a normal heart database (as per the 4D-MSPECT method) [157]. In clinical comparisons, results correlate well with semi-quantitative expert visual analysis (R=0.82) [158] [159]. • In the Yale CQ software, maximum circumferential count profiles are again used to create polar maps which are compared to a normal heart database [160]. Defect sizes are consistently underestimated and therefore a correction factor is applied to the results [161]. • Another method developed at Cedars-Sinai Medical Centre, the QPS software, still requires the comparison of a polar map with a normal heart database, but the sampling used to create the polar map is more indicative of the 3-D volume of the LV [162] [163]. The method presumes the LV is shaped like an ellipsoid rather than a simple cylinder with a hemi-spherical base, and therefore uses ellipsoid sampling. It also uses an average of the entire count profile between the endocardial and epicardial surfaces to create its count profile, rather than just the maximum or central value. Clinical validation shows that the sensitivity and specificity of the method is different for rest and stress studies, and for male and female groups [164]. Reproducibility of the measurement of myocardial infarct size using the program is excellent (R=0.999) [162]. • A novel method that was never developed into commercially available clinical software is the PERFIT method. Each investigated heart is reshaped to fit a 3-D reference template. This reshaped heart is then compared to a database of normal hearts also fitted to this template, with a region being defined as a defect if it contains less counts than the mean of the database minus 2 standard deviations [165]. In this way the size, severity and location of myocardial defects can be determined using a 3-D normal heart database without relying on the approximations intrinsic to the creation of a polar map. Each commercially available software technique relies on a 2-D solution to a 3-D problem, the creation of a polar map which, due to its 2-D nature, will always involve some degree of approximation due to limited sampling and volume rescaling factors. All methods except one require the creation of normal heart databases, which is a procedure not versatile enough to accommodate data sets from different SPECT systems and different reconstruction techniques [166]. Comparisons of data sets acquired at different clinical centres or using different SPECT corrections are therefore difficult. Different databases are required for male and female patients, but because of the huge variation seen in body type these average databases provide very approximate comparisons, resulting in low test specificities Chapter 2: Background Information and Literature Review 40 [140]. Before any software technique that relies on comparisons with a normal heart database can be used to measure myocardial infarct size, substantial additional work is required. This is due to the fact that 20 to 30 patients with a low likelihood of CAD are required to create each normal heart database, and the fact that separate databases are required for each patient gender, radiopharmaceutical, imaging protocol, type of stress test, camera system, reconstruction technique, etc [167]. Due to the concerns listed above relating to the use of any presently available myocardial perfusion quantitation software, it was decided to design new software for use in this thesis. The new software, iQuant, works entirely in 3-D and therefore does not require the creation of a polar map. The software does not require the use of a normal heart database and therefore allows comparisons of myocardial infarct size resulting from data sets reconstructed using different SPECT corrections. 2.4.2.6 The effect of SPECT corrections on the accuracy of myocardial perfusion measurements Most problems involved in the accurate determination of the thickness of the myocardial wall and the size of a myocardial perfusion infarct, result from the effects of photon attenuation, photon scatter and distance-dependent resolution loss. To provide data sets of sufficient quality to deliver the diagnostic information required, it may therefore be necessary to correct for these effects during SPECT reconstruction. Previous phantom and clinical studies have investigated the effect on myocardial quantitation of reconstructing SPECT data sets using various corrections. For example, patient-specific AC is shown to restore uniformity to the polar map in computer simulation and phantom studies [168], and to increase diagnostic accuracy in clinical studies [169] [170]. However, it is also shown to increase the interference of hepatic activity in the inferior wall of clinical studies (number of patients N=47) [171]. In computer simulation and phantom studies DRC is shown to improve resolution and contrast, but also to reduce signal-to-noise ratio [168]. Energy window SC techniques are shown to improve image contrast in clinical studies but also to decrease the signal-to-noise ratio (N=30) [24]. Energy window SC techniques are also shown to improve the delineation of myocardial defects (N=100) [172]. The SPSF SC technique is shown to improve the size of myocardial perfusion defects in phantom studies [173]. The use of patient-specific AC together with 'ideal' SC is shown to decrease hepatic interference in computer simulations [174]. Patient-specific AC and energy window SC is shown to increase specificity but decrease sensitivity in the measurement of myocardial defect severity, and to generate false anterior wall defects in clinical studies (N=607) [175]. The use of patient-specific AC, DRC and energy window SC together, is shown to improve the detection of CAD both in the anterior and septal walls of clinical studies (N=43) [176], and in the inferior and lateral walls (N=100) [177] [178]. Although discussion in the recent past about the routine use of AC for clinical myocardial perfusion studies has been animated [179] [180], present thinking (derived from the studies detailed above) is that AC, DRC and SC significantly improve the diagnostic value of myocardial perfusion images, and that additional development of these methods will further improve their diagnostic accuracy [181] [182] [183]. As no myocardial quantitation studies have been carried out using DRC modelled from a depth-Chapter 2: Background Information and Literature Review 41 dependent Gaussian function, or the APD/APDI method of SC, this thesis tests their ability (together with patient-specific AC) to accurately determine the diagnostic parameters of myocardial wall thickness and myocardial infarct size. 42 C H A P T E R 3 M E T H O D S - C R E A T I O N O F D A T A 3.1 Dos imet ry 3.1.1 Introduction Accurate knowledge ofthe biodistribution of radioactivity is required to correctly calculate dosimetry. Biodistribution is usually assessed using planar acquisitions, whether whole body (acquired from a camera scanning the length of the patient) or static (a smaller field of view acquired from a static camera). Two methods can be employed to assess planar acquisitions. However, more accurate information can be obtained from SPECT acquisitions. When both emission and transmission SPECT data sets are available, several levels of accuracy in the quantitation of activity distribution can be achieved by using attenuation correction (AC), detector response compensation (DRC) and scatter corrections (SC) during reconstruction. To determine what level of accuracy in quantitation of activity distribution can be achieved using these methods, three types of experiments were performed: 1) The first experiments used a computer model of a simple 2-D (single slice), attenuating, radioactive, transaxial body slice containing tumors. From this slice, 1-D anterior and posterior planar acquisitions were simulated. The activity originating in the tumors was calculated from these projections. This preliminary study was performed to give an indication of the error arising from biodistribution information gathered from planar acquisitions and simple calculations. 2) A more comprehensive and clinically relevant simulation was then carried out to compare the accuracy of biodistribution derived from planar acquisitions using simple and more complex calculations, and from SPECT acquisitions reconstructed using AC and DRC. This simulation used the MCAT computer phantom and the SimSET Monte Carlo simulation of the nuclear medicine acquisition process. The phantom was a 3-D model of the human thorax containing organs with suitable attenuation and activity values, and two tumors. 3) To fully test SPECT reconstruction techniques and their effect on the quantitative accuracy of dosimetry calculations, a series of phantom experiments was performed using the Siemens E-cam dual-headed camera with Profile transmission source. Two phantoms were scanned, a Thorax phantom to which two tumors had been added, and a Jaszczak SPECT phantom containing a series of radioactive spheres. Both phantoms were scanned using a) static planar, b) whole body planar and c) SPECT acquisitions, the latter of which were reconstructed using a number of different techniques. The resulting biodistribution estimates were compared. Chapter 3: Methods - Data Creation 43 The isotope m Tc is used in dosimetry studies of new Tc-labelled imaging radiopharmaceuticals, and also as the imaging isotope that mimics the biodistribution of therapy radiopharmaceuticals. Other isotopes, such as 1 1 1ln and 1 2 3 l , are also used to mimic the biodistribution of therapy radiopharmaceuticals for imaging and therefore dosimetry purposes. However, the studies in this thesis were only performed using 9 9 m T c as it is readily available and cheap. The conclusions drawn from the results of 9 9 m T c studies will be largely applicable to the use of these additional isotopes. The only variations will be due to the slightly higher energy of the y-radiation emitted from 1 1 1ln (171 keV and 245 keV) and 1 2 3 l (159 keV) compared to 9 9 m T c (140 keV). This will minimally reduce the attenuating effect of the medium through which the photons pass, but in no way negate the need for attenuation correction. Due to the higher energies involved in 1 1 1ln imaging, a Medium Energy (ME) collimator is used in preference to the Low Energy, High Resolution (LEHR) collimator used in 9 9 m T c or 1 2 3 l imaging. The ME collimator has larger diameter holes than the LEHR collimator, increasing the resultant distance-dependent resolution loss. Therefore detector response compensation is even more necessary. 3.1.2 Simple 2-D simulation The simple 2-D simulation was designed to estimate the error arising from biodistribution information gathered from planar acquisitions and simple calculations. The analysis was performed in the MATLAB environment using a 64 x 64 matrix to simulate a transaxial slice through a patient's body. An activity and attenuation factor was assigned to each pixel (1cm2 in area) to describe a slice through a body of thickness 20 cm and width 40 cm. Five separate cases were simulated, each with a single 4 cm diameter tumor added in one of five positions (Figure 3.1). Tumor to background body activity ratios of 6:1 and 1:0 (no background activity) were simulated for each tumor position, giving a total of 10 investigated situations. Figure 3.1: Transaxial body slice with five tumor locations, used in the 2-D study. The body was assumed to have a uniform linear attenuation coefficient specific to the isotope 9 9 m T c and the surrounding air was assumed to be non-attenuating. The linear attenuation coefficient of 9 9 m T c was taken to be 0.15 cm"1, corresponding to the attenuation coefficient of a 140 keV photon in water, Chapter 3: Methods - Data Creation 44 which is (as discussed previously) a good approximation to the coefficient in soft tissue [184]. The narrow beam attenuation coefficient was used as Compton scatter was not simulated in this study. Acquisitions were simulated for the anterior (lA) and posterior (lP) projections of each body slice. Using both these images the simple method (described in section 5.1.1.1 Biodistribution calculations -Planar data - Simple method) was used to calculate the biodistribution of activity in each slice. 3.1.3 Comprehensive simulation This more comprehensive simulation was performed using the MCAT computer phantom [185] to compare methods of absolute activity estimation based on planar and tomographic acquisitions. The model of the female thorax was built on a 128 x 128 x 128 matrix, with a pixel dimension of 3.6 mm (see Appendix A1 for MCAT parameter details). Each organ contained within the thorax was assigned a linear attenuation coefficient to describe the penetration of 9 9 m T c photons into a tissue of that specific density. Two tumors of 4 cm diameter were added to the thorax, one in the abdomen (7 pixels below the right lung, 5 pixels anterior to and right of the body centre), and one on the lateral surface of the right lung (half way between its apex and base). Activity was assigned to each organ and tumor to simulate the relative organ activities approximately 24 hours post administration of the radioimmunoconjugate Y90-Zevalin (an anti-CD20 MAb) [86], see Table 3.1. The total activity of each tumor was 8.68 MBq. Table 3.1: Organ activity concentrations used within the MCAT phantom. Organ Activity concentration (kBq/cm3) Volume of organ (ml) Tumor 259 34 Spleen 74 175 Liver 55.5 1794 Lungs 18.5 3838 Background 5.2 33134 The Monte Carlo simulation program SimSET version 2.6.2.3 [186] was used to predict the path of each emitted photon through the MCAT phantom to the gamma camera (including its attenuation and scatter). The simulation used variance reduction to decrease the time required for generation of the data set; it only traced the photon flight paths that were likely to be detected by the camera. However, an adequate number of photon histories (approximately 20x10 9 ) were simulated to obtain noise characteristics corresponding to an experimental scan, as recommended by the SIMSET documentation [187]. The simulated acquisition included a geometric collimator response function for a parallel hole, Low Energy, High Resolution (LEHR) collimator, installed on a single 60 by 60 cm camera head (large enough to ensure that the patient remained fully within the detector's field of view). The energy Chapter 3: Methods - Data Creation 45 response of the detector was modelled as a Gaussian with full-width at half-maximum (FWHM) equal to 10% of the incident photon energy, and a 20% energy window was used in the detection process. The simulated detector was rotated in a circular orbit in a clockwise direction (CW), with a start angle of -90° (Siemens convention as illustrated in Figure 3.2). A 23.04 cm radius of rotation gave a minimum of 5 cm clearance at each side of the torso. A total of 180 projections evenly spaced over 360° were acquired for 20 s each. The projection matrix was 128x128 with 3.6 mm bins. Figure 3.2: The Siemens convention for camera position. View facing the dual headed Siemens E-cam camera (the SimSET detector only has one head). SPECT reconstructions were carried out as described in section 3.4 SPECT Reconstruction, and from the resultant images the biodistribution of activity was measured as described in section 5.1.1.3 Biodistribution calculations - SPECT data. Planar acquisitions were created from a SimSET simulation of four projections, corresponding to angles of 0°, +180°, +90° and -90°, with acquisition times of 20 min each. This provided the anterior and posterior images for tumour activity calculations, and the lateral images from which patient and tumour thickness could be measured. The biodistribution of activity from the planar acquisitions was measured using two separate methods, one simple as described in section 5.1.1.1 Biodistribution calculations -Planar data - Simple method and the other more comprehensive as described in section 5.1.1.2 Biodistribution calculations - Planar data - Complex method. For these calculations a broad beam linear attenuation coefficient of 0.12 cm"1 for 9 9 m T c photons in water was used for the body, to help compensate for photon scatter in addition to attenuation. To find the sensitivity (efficiency in counts/min/kBq) of the acquisition process simulated by SimSET, a phantom was created consisting of a one voxel point source in air (with no surrounding attenuating medium). The point was located off axis in a central slice and contained 10.8 MBq of activity emitting 140 keV photons. SimSET was used to simulate the acquisition of this point using identical parameters to those used for the planar acquisition of the thorax, specified above. 0' +180' Chapter 3: Methods - Data Creation 46 3.1.4 Phantom experiments To fully test SPECT reconstruction techniques and their effect on the accuracy of quantitative dosimetry calculations, physical phantom experiments were performed. The phantom experiments used a Jaszczak SPECT phantom (Data Spectrum Corp., Hillsborough, NC) and a Thorax phantom (Data Spectrum Corp., Hillsborough, NC). The Jaszczak phantom contained six spheres filled with radioactivity, and of diameters 6.5, 8, 9, 11, 16 and 19 mm (volumes of 1, 2, 3, 6, 16, 29 ml), see Figure 3.3. Figure 3.3: The end view (from the head of the bed) of the Jaszczak phantom showing the positioning ofthe hot spheres and their numbering. The Thorax phantom contained lungs inserts filled with Styrofoam beads, and a spine insert made of bone-equivalent material to simulate the different attenuation properties that occur in the body [188]. The phantom also contained a cardiac insert. Two cylinders where placed in the thorax to simulate tumors: an 8 ml cylinder (diameter 35 mm) was attached to the underside of the right lung, and a 12 ml cylinder (diameter 50 mm) attached to the anterior of the spine 50 mm below the base of the lungs. These cylindrical bottles were tested with ink dye in a volume of water to ensure the tightness of their seals. The tape used to attach the cylinders to the phantom was also tested to ensure its adhesive properties when submerged. Two 1 L water bags where taped to the anterior side of the thorax phantom to simulate attenuation caused by significant mammary tissue (Figure 3.4). An additional water bag was taped to the base of the phantom to simulate the diaphragm. A syringe of activity (effectively a point source) was used as a calibration source to assess the sensitivity of the system. The activities of 9 9 m Tc sodium pertechnetate which were added to the phantoms were based on the activity concentrations observed at 24 hours post administration of the radioimmunoconjugate Y 9 0-Zevalin [86]. These values are presented in Table 3.2 together with the activities at the time of acquisition. The phantoms were agitated for a minimum of 5 minutes prior to measurement to ensure uniform mixing ofthe administered activity. Jaszczak phantom scanning Chapter 3: Methods - Data Creation 47 Thorax phantom heart insert right lung insert 8 ml t u m o r water bags to simulate mammary t issue -water bag to simulate d iaphragm 12 ml tumor spine insert Figure 3.4: Positioning o f t h e water bags on the Thorax phantom. Table 3.2: Activity of 9 9 m T c sodium pertechnetate administered to Thorax and Jaszczak phantoms. Region of interest Activity concentration (kBq/ml) Total activity at time of acquisition (kBq) Static planar Whole body planar SPECT Thorax 12 ml tumor 250 2682 2958 2367 8 ml tumor 250 1931 1909 1528 Heart 50 - - -Background 5 - - -Jaszczak Sphere 6 250 4459 4724 3929 5 250 2399 2541 2113 4 250 1192 1263 1050 3 250 419 443 369 2 250 267 283 235 1 250 111 118 98.1 Background 5 - - -Calibration Point source - 7290 7040 7550 The phantoms where placed on the scanning bed with the Thorax phantom simulating a supine patient with his head towards the camera, and the Jaszczak phantom posit ioned superior to this (as if it was the patient's head), see Figure 3.5. Chapter 3: Methods - Data Creation 48 Figure 3.5: The Jaszczak and Thorax phantoms set up on the scanning bed. The following scans of the phantoms were acquired on the dual-headed Siemens E-cam gamma camera with the Profile transmission source and the low energy, high resolution (LEHR) collimators: 1. Simultaneous anterior and posterior whole body planar scan with 4 cm/min camera movement (29 min total scan time) covering both phantoms, a 20% energy window at 140 keV and a 256 x 512 matrix. 2. Static planar scans, with a 20% energy window at 140 keV and a 256 x 256 matrix. Anterior and posterior acquisitions for 20 min each covering (a) the Jaszczak phantom, (b) the Thorax phantom, and (c) the calibration source with the acquisition length reduced to 5 minutes. Left and right lateral acquisitions for 10 min each covering (a) the Jaszczak phantom, and (b) the Thorax phantom, to allow measurement of phantom and tumour thickness for both whole body and planar calculations of tumour activity. 3. SPECT scans were acquired with the cardiac acquisition protocol. This involved simultaneous emission and transmission acquisitions, 64 projections of 40 s, four energy windows (8% at 86 keV, 20% at 100 keV, 12% at 116 keV, 20% at 140 keV), and a 128 x 128 matrix. The camera heads were positioned at 90° to each other, with start angles of 45° (right, anterior oblique projection) and -45° (left anterior oblique projection), see Figure 3.2. Each head acquired projections over 90° in a non-circular orbit in the counter-clockwise direction (CCW), covering (a) the Jaszczak phantom, and (b) the Thorax phantom. The pixel dimensions were 4.8 mm for a 128 x 128 matrix, giving a reconstructed voxel volume of 0.111 cm3. It should be noted that the positioning of the two camera heads at 90° to each other and an acquisition of only 180° (cardiac protocol) may not prove optimal for dosimetry scans. Ideally the cameras should be placed at 180° to each other and rotated a full 360° around the subject. However, the E-cam camera only performs transmission scans for a 90° head configuration and for cardiac protocols. Chapter 3: Methods - Data Creation 49 SPECT reconstructions were carried out as described in section 3.4 SPECT Reconstruction, and from the resultant images the biodistribution of activity was evaluated as described in section 5.1.1.3 Biodistribution calculations - SPECT data. The biodistribution of activity from the planar acquisitions (both static and whole body) was measured using the method described in section 5.1.1.2 Biodistribution calculations - Planar data - Complex method. A spatial filter (Butterworth, cut-off 0.5, order 5) was applied to all images before regions of interest were drawn. The exception to this was the SPECT reconstructions that included DRC, this correction is in essence a spatial filter, and therefore no post-reconstruction filter was applied to these data sets. Chapter 3: Methods - Data Creation 50 3.2 Myocardial Wall Thickness Myocardial wall thickness, as assessed from myocardial perfusion studies, was used to investigate the absolute quantitation of SPECT reconstruction techniques. As previously discussed, when data sets are reconstructed with FBP, myocardial quantitation software programs require separate normal heart databases or thresholds for each patient gender, radiopharmaceutical, imaging protocol, type of stress test, camera system, reconstruction technique, etc. In order to determine if this is also the case when corrections are applied, myocardial wall thickness measurements were compared between these groups using the experimental and clinical data sets acquired to study myocardial wall thickness and reconstructed using AC and DRC. 3.2.1 Computer Simulations The myocardial wall thickness of myocardial perfusion computer simulations was used to compare the quantitative differences between a static heart and a beating heart. The mathematical cardiac-torso phantom MCAT [185], was used to model the activity distribution in the thorax of a standard sized female on 128x128x47 matrix, both with a static [189] and a beating heart [190] [191] (see Appendix A2 for MCAT parameter details). For each model the thickness of the myocardial apex was half that of the remainder of the left ventricle (LV) myocardium to reflect the clinical situation [192]. The activity distribution was modelled on a standard clinical injected 99mTc-Sestimibi activity of 925 MBq. The LV myocardium contained an activity concentration of 148 kBq/cm3, with the surrounding background tissue containing 37 kBq/cm3 (one quarter of the viable myocardial concentration) and the lungs 18.5 kBq/cm3 (one eighth of the myocardial Concentration). The right ventricle (RV) myocardium contained half the concentration of the LV myocardium (74 kBq/cm3), and the left and right atrium tissue contained half the concentration of the RV (37 kBq/cm3). The model containing the static heart was 3-D, and the model containing the beating heart was 4-Q with the fourth dimension describing the 16 time frames of the cardiac cycle. The Monte Carlo code SimSET version 2.6.2.3 [186] was used to simulate a SPECT acquisition of each MCAT model using the method described in section 3.1.3 Dosimetry - Comprehensive simulation. Certain parameters were altered to provide an simulation comparable to a clinical myocardial perfusion study. The LEUR collimator was replaced by a Low Energy, Ultra High Resolution (LEUHR) collimator (standard use in cardiac SPECT as resolution is considered more important than sensitivity in this situation). A total of 64 projections were acquired over 180° for 20 s each. Approximately 13x109 photon histories were simulated to obtain noise characteristics corresponding to an experimental scan. To provide statistical variation, each data set, once reconstructed, was reorientated manually 5 times, creating 5 unique data sets. It was found that this procedure provided statistical variation equivalent to acquiring each model 5 times: the MCAT phantom with a static, healthy heart, acquired just once through Monte Carlo simulations, was reorientated 5 times. Myocardial wall thickness was measured using a range of boundary conditions, giving mean values of 2.78 + 0.10 to 6.39 + 0.21 Chapter 3: Methods - Data Creation 51 voxels (± Confidence Intervals of 95%). Five separate acquisitions of the Thorax phantom (which has a wall thickness identical to the MCAT phantom) containing no infarcts, were reorientated separately. Myocardial wall thickness measured for the same range of boundary conditions, gave mean values of 2.09 + 0.15 to 6.47 ± 0.28 voxels. The difference between these sets of values was not statistically significant (p<0.05). 3.2.2 Phantom Experiments The measurement of the myocardial wall thickness of the Thorax phantom (Data Spectrum Corp.) was used to investigate the absolute quantitation of SPECT reconstruction techniques. It was also used to assess variations arising from patients (specifiable in a phantom), acquisition protocols and post reconstruction processing: • Background activity variations - investigated using myocardium to background ratios of 7:1, 4:1 and 3:1. • Acquisition statistics (signal-to-noise ratio) differing between stress and rest acquisitions -investigated using different acquisition times of the same phantom. An acquisition time per projection of 20s to simulate stress study statistics and 5s per projection to simulate rest study statistics. • Application or not of an acquisition zoom - investigated using emission only acquisitions of the phantom as the Siemens E-cam does not allow for the zoomed acquisition of the transmission source. • Spatial filter type - investigated using a Gaussian ([3,3,3] kernel size and standard deviation of 0.75), a sharp Butterworth (cut-off frequency 0.55, order 5), and a smooth Butterworth (cut-off frequency 0.3, order 10) filter. The filters chosen for investigation were selected from published investigations of myocardial perfusion defect size [193] [194] [15] [39] [178]. • Interpolation onto a larger matrix - investigated by cubically interpolating a 128 x 128 x 128 reconstructed data set onto a 256 x 256 x 256 matrix. Thorax phantom volumes were measured to be 62 ml for the LV chamber, 104 ml for the LV myocardium, and 5568 ml for the background (total thorax cylinder minus lungs, total heart and spine). The 9 9 m T c activity inserted into the myocardium of the Thorax phantom was representative of the activity found in clinical studies. The value was determined from 14 standard clinical cardiac studies reconstructed using OSEM+AC+DRC. The mean number of counts originating in the myocardium of 7 clinical rest studies was found to be 31 counts per voxel, whereas the mean from 7 stress studies was 125 counts per voxel. An activity of 30 MBq of 9 9 m T c was added to the myocardium of the Thorax phantom which contained water but no activity in the background regions. This was scanned using the standard clinical cardiac protocol (with a time per projection of 20 s), and reconstructed using OSEM+AC+DRC. The mean number of counts originating in the myocardium was found to be 131 per Chapter 3: Methods - Data Creation 52 voxel. Therefore, for subsequent experiments, the activity added to the myocardium of the Thorax phantom was 30 MBq, representative of clinical stress studies. Using the same phantom, acquisitions representative of clinical rest studies were produced by reducing the acquisition time per projection from 20 s to 5 s. Transmission scans acquired simultaneously with these reduced time acquisitions were discounted, due to their poor and unrepresentative statistics. The transmission scans acquired during the stress acquisitions were used instead, (the phantom was not moved between these two acquisitions). In a similar way, the absolute activity of 9 9 m T c inserted into the background region of the phantom was representative of the activity found in clinical studies. Measurements of 14 clinical cardiac studies showed myocardium to background activity ratios ranging from 3:1 to 7:1, with the group mode, median and mean values coinciding at 4:1. These three ratios, namely 3:1, 4:1 and 7:1, were used as the activity ratios to be investigated in the Thorax phantom experiments. The resultant activity concentrations in the Thorax phantom were 300 kBq/ml for the LV myocardium, 100 kBq/ml for the background region for experiments with a myocardium to background activity ratio of 3:1, 75 kBq/ml for the background region at 4:1 and 43 kBq/ml for 7:1. The background region included the LV chamber. Two 1 L water bags where taped to the anterior side of the phantom to simulate attenuation caused by significant mammary tissue. The phantoms were agitated for a minimum of 5 minutes prior to being positioned on the scanning table to ensure uniform mixing of the administered activity. Additionally the phantom with the 4:1 myocardial to background activity ratio was used to investigate acquisition zoom. The phantom was acquired with a zoom factor of (i) 1.45 and (ii) 1.00 (no zoom). For this investigation no transmission scans could be acquired and therefore the attenuating water bags were removed. The phantoms were scanned on the Siemens E-cam camera with Profile transmission system (where applicable), using the standard cardiac acquisition protocol (as detailed in the previous section), with an acquisition time of 20 s per projection. To provide statistical variation five scans were acquired of each for these 8 situations, with the phantom repositioned between each acquisition. Due to the consecutive acquisition of 40 scans of an isotope (99mTc) that decayed with a half-life of 6.02 hours, a decay correction was applied to the projection time to ensure comparable count statistics in each data set. 3.2.3 Clinical Data A database of myocardial perfusion studies was created from all consenting patients scanned with the transmission source on the Siemens E-cam camera at Vancouver General Hospital. Using categorization based on medical history and the results of stress electrocardiography (ECG) [73], 38 of these patients were determined to have a less than 5% likelihood of CAD. These 38 rest and 38 stress Chapter 3: Methods - Data Creation 53 studies were therefore considered to show normal myocardial perfusion, and were subsequently used for analysis. The myocardial wall thickness values of these 76 clinical data sets were used to investigate the absolute quantitation of SPECT reconstruction techniques, and the wall thickness dependency on variations commonly seen clinically. Variations included: • Patient gender - investigated by comparing the male and female groups in the database. • Liver interference - investigated by comparing studies containing no obvious activity lying close to the myocardium, to those with a close lying active liver, gut, stomach or gall bladder. • Acquisition statistics - investigated by comparing the rest and stress studies in the database. Due to the differences in injected activity the total counts in a rest study are usually about 25-30% of that in a stress study. The proportion of the injected activity taken up by the myocardium also differs between patients, resulting in varying acquisition statistics. • Type of stress test performed - investigated by comparing the stress tests performed on a treadmill to those involving a pharmacological administration. However, the resultant statistical power of this comparison was low. • Spatial filter type - investigated by comparing a sharp Butterworth (cut-off frequency 0.55, order 5) to a smooth Butterworth (cut-off frequency 0.3, order 10) filter. Patients were scanned on the Siemens E-cam camera with Profile transmission system, using the standard cardiac acquisition protocol. For the rest study 370 MBq 99mTc-Sestamibi was administered and for the stress study 1100 MBq was administered. Chapter 3: Methods - Data Creation 54 3.3 Myocardial Infarct Size Myocardial infarct size, as assessed from myocardial perfusion studies, was used to investigate the relative quantitative accuracy of SPECT reconstruction techniques. 3.3.1 Computer Simulations As previously described for the study of myocardial wall thickness (section 3.2.1 Myocardial wall thickness - Computer simulations), the mathematical cardiac-torso phantom MCAT [185], was used to model the activity distribution in the thorax of a standard sized female, both with a static [189] and a beating heart [190] [191]. The activity distribution was again modelled on a standard clinical injected 9 9 m T c activity of 925 MBq. In this case however, myocardial infarcts were added to the models (see Appendix A3 for MCAT parameter details), each containing an activity concentration of 60 kBq/cm3 (0.4 of the viable myocardial concentration). Four models were produced with medium sized myocardial infarcts positioned in the anterior, inferior, lateral and septal walls. The medium infarct was 13.9% of the total static LV myocardium, encompassing 90° of the LV, positioned half way along the wall in question, and taking up half the length of the wall (Figure 3.6). Two complete sets of models were created, the first with a static heart and the second with a beating heart. Infarct position Short axis view Vertical long axis view Horizontal long axis view Anterior wall <s> (f\ Inferior wall Lateral wall Septal wall ^5> Figure 3.6: Locations of MCAT phantom medium infarct (13.9% of total myocardium). Chapter 3: Methods - Data Creation 55 The Monte Carlo code SimSET version 2.6.2.3 [186] was used to simulate the SPECT acquisitions of the MCAT models (as detailed previously). To provide statistical variation, each data set, once reconstructed, was reorientated manually 5 times. 3.3.2 Phantom Experiments Phantom experiments were carried out using the Thorax phantom, described previously, with the addition of myocardial infarcts (provided with the phantom from Data Spectrum Corp.). The infarcts sizes were: a) very small (2.15 ml, equivalent to 3.6% of the total myocardium), b) small (5.5 ml, 5.2%), c) medium (11.4 ml, 12.5%), and d) large (16.9 ml, 17.7%). These volumes included the plastic wall of each infarct insert. Although an infarct of only 2.15 ml would not be considered clinically significant, it was included to determine if its presence could be detected in reconstructed images. A very large infarct could not be constructed from the available equipment and was therefore not included in the phantom experiments. Relative activity concentrations administered to the Thorax phantom were representative of those found in clinical studies. As in section 3.2.2 Myocardial wall thickness - Phantom Experiments, 14 patient studies were analysed to determine the mean count value occurring in areas of background, liver, viable myocardium and myocardial defect. The mean activity concentration ratios were found to be: Viable myocardium to background 4:1 Viable myocardium to liver 1:1 Viable myocardium to myocardial defect 3:1 The resultant activity concentrations added to the Thorax phantom were 300 kBq/ml for the LV myocardium, 75 kBq/ml for the background region including the LV chamber, and 100 kBq/ml for the myocardial infarcts. Initially 16 phantoms were acquired, with each ofthe four infarct sizes positioned in the (a) anterior, (b) inferior, (c) lateral, and (d) septal walls of the LV. A further three phantoms were acquired containing the small infarct in the inferior wall for: (1) an infarct activity concentration of 50 kBq/ml, slightly below that of background, (2) an infarct activity concentration of 200 kBq/ml, greater than one half that of the myocardium, and (3) the original infarct activity with the addition of a close lying liver containing an activity concentration equal to that of the myocardium. The liver, of volume 295 ml, was modelled by inserting a cylindrical bottle taped perpendicular to the spine and approximately 1 cm from the apex of the myocardium. In each case water bags were used to simulate the presence of breasts and each phantom was agitated for a minimum of 5 minutes prior to being scanned to ensure uniform mixing of the administered activity. The phantoms were scanned on the Siemens E-cam with Profile transmission system using the standard cardiac acquisition protocol, previously detailed. The acquisition projection times, initially 20 s each, were chosen to generate data sets with the statistics commonly found in clinical stress scans, and Chapter 3: Methods - Data Creation 56 were adjusted for radioactive decay as time progressed. In this study each phantom was acquired only once, however to provide statistical variation, its reconstruction was reoriented manually 5 times, creating 5 unique data sets. 3.3.3 Software validation The iQuant software for myocardial quantitation was developed for this thesis. As the measurement of myocardial infarct size is a complex procedure, it was necessary to test the accuracy and reliability of iQuant in this context. To test the accuracy of the iQuant method it was necessary to compare its measurement of infarct size with the known truth. Unlike other comparisons with the truth carried out in this work, it was necessary to know exactly what was being measured, not just the object from which the data set under investigation was acquired. Therefore it was necessary to measure the infarct size of the object itself, not an acquisition of the object as this would insert essentially unknown variables such as the random statistics of radioactive decay, the effect of pixelization, and the accuracy of the reconstruction technique. Therefore the accuracy of the iQuant method was determined using the original, beating heart MCAT model (previously described in section 3.3.1 Myocardial infarct size - Computer Simulations), with no SimSET acquisition simulations. The true size of the medium infarct in the beating heart model varied from 13.8% to 19.1% throughout the cardiac cycle, with an average value over time of 15.4% of the total myocardium. Four MCAT models, each containing the infarct positioned in a different LV wall, were used in this analysis. Further validation of the software was carried out using additional phantom experiments and clinical data sets. To test the ability of iQuant to measure myocardial infarct size in reconstructed nuclear medicine data sets, the reliability (also known as the precision or reproducibility) was determined. This analysis was performed using the Thorax phantom, containing the small defect positioned on the mid point of the inferior wall. The phantom was scanned 5 times, repositioned between each acquisition. A time per projection of 20 s was used to simulate clinical stress statistics. After reconstruction with OSEM+AC+DRC and reorientation, the data sets were analysed by three independent observers and the results compared. To compare infarct size measurements determined using the iQuant software with those obtained from other, well established, myocardial quantitation software programs, both phantom and clinical data sets were used. Firstly the iQuant software was compared to the Mayo Clinic myocardial quantitation software [142]. This study was designed and specified by the Mayo Clinic. The study was carried out on an elliptical thorax phantom (Mayo Clinic) containing solid myocardial infarcts in various positions in the myocardial walls. The infarct sizes were 6% of the total myocardium, 10%, 21%, 29%, 40%, 50%, 61% and 71%. Nine emission scans were acquired from the phantom, one for each size of infarct and one with no Chapter 3: Methods - Data Creation 57 infarcts. As part of the multi-centred EMERALD study [146], these data sets were sent to the Mayo Clinic for myocardial infarct size measurement. They were also analysed using iQuant, and the results were compared. The iQuant software was also compared to the 4D-MSPECT program [148]. As part of a separate clinical trial, myocardial perfusion rest studies were acquired from 22 patients scanned 5-7 days post myocardial infarction (Ml). Thirteen out of the 22 studies were performed with transmission acquisitions. These clinical data sets from patients with known diagnosis of Ml, reconstructed using FBP, were used to compare myocardial infarct size measurements obtained from iQuant and from 4D-MSPECT. Chapter 3: Methods - Data Creation 58 3.4 SPECT Recons t ruc t i on All reconstructions were performed using oSPECT software version 7.2 [57] developed at MIRG. The software allows different combinations of reconstruction algorithms and SPECT corrections to be applied to data sets. The AC incorporated within oSPECT uses a patient specific map of attenuation coefficients [16]; the analytical calculation of SC is based on the Klein Nishina formula for Compton scatter [18]; and the correction for DRC is modelled by a 3-D Gaussian profile cone [57]. All corrections were described in more detail in section 2.3 Corrections for photons attenuation, photon scatter and distance-dependent resolution loss. Each iterative reconstruction using the Ordered Subset Expectation Maximization (OSEM) algorithm, was computed using 5 iterations together with 8 subsets. These values were selected from published investigations of myocardial perfusion defect size [15] [39] [195]. Previous experiments have shown that attenuation maps often require segmentation to improve image quality [196]. In this study all maps were segmented for consistency, and a Butterworth spatial filter (cut-off 0.3, order 5.0) was applied. The only exception to this was for the attenuation maps that originated from the MCAT phantom and therefore those used for computer simulation studies. In these cases a lighter Butterworth filter (cut-off 0.5, order 10) was applied to remove sharp edges but to retain the detailed structure of the map. Unless SC was to be applied during reconstruction, attenuation maps were rescaled from narrow to broad beam attenuation coefficients (from 0.15 cm"1 to 0.12 cm"1 for photons of 140 keV in water) to partly compensate for photon scatter. For SC to be incorporated into the reconstruction technique, the contribution of scatter to emission projections had to be estimated. This was done using APDI software [197], developed at MIRG. In oSPECT, scatter projection estimates could then be incorporated into each forward projection iteration of OSEM. Eight iterations were used together with 8 subsets, this increase in the number of iterations was due to the increased complexity of the computations. Unless specified otherwise, each set of SPECT projections was reconstructed using the following combinations of reconstruction algorithms and SPECT corrections: • Filtered Back-Projection (FBP) • OSEM • OSEM + AC • OSEM + DRC • OSEM + AC + DRC • OSEM + AC + DRC + SC For the myocardial wall thickness comparisons, reconstruction of data sets was carried out using OSEM+AC+DRC unless otherwise stated. For the comparison of data sets acquired with and without an acquisition zoom, the data sets were reconstructed using OSEM+DRC. Scatter correction was not used in the reconstruction of computer simulated data sets. Chapter 3: Methods - Data Creation 59 3.4.1 Reorientation All simulation, phantom and clinical myocardial perfusion studies performed for this work were reorientated using SPECTacular software developed at MIRG on an IDL platform. The program requires the user to specify the centre of the LV (the point of rotation) and to draw the long axis of the LV in 2 projections (to define the rotation angles). The program then creates a new reorientated matrix using a linear interpolation of the 8 closest voxels of the old matrix (cubic interpolation). Each voxel carries a weighting factor dependent on its distance from the new voxel centre. Cubic interpolation is accurate as it takes information from each neighbouring voxel, however it increases the spatial smoothness of the image. The iQuant software can be used to measure transaxial (the original orientation) as well as reorientated data sets, so as to avoid the aliasing errors associated with reorientation interpolation. However, as the recognizable shapes and positions of the reorientated LV, RV and liver significantly assist the operator during the analysis process, and preliminary tests showed that quantitative measurements made from reorientated data sets were more accurate than those made from the original transaxial data sets, it was decided to perform the analysis using reorientated data sets only. No spatial filters were applied to data sets whose reconstruction included DRC as this is in itself a type of filter. A light Butterworth filter (cut-off 0.55, order 5) was applied to all other reorientated data sets. 60 CHAPTER 4 METHODS - SOFTWARE DESIGN 4.1 ImageTools The MIRG ImageTools software was written to help visualize, evaluate and quantify variations that are observed in clinical myocardial perfusion SPECT images reconstructed using different techniques [198] [199]. The parameters under investigation were spatial resolution, statistical noise and image artefacts. ImageTools is written on a MATLAB platform and operated using a graphical user interface (GUI). It allows input from 2-D images and 3-D data sets. A user specified spatial filter can be applied to the input data set. From its main window or interface, the following actions can be performed: • As most of the tools use a 2-D image input, a secondary window allows the selection of 2-D images from 3-D data sets. • Images can be manipulated by rotation or reflection about their central axis. • To investigate spatial resolution, amplitude profiles are created along a specified line intersecting the myocardial wall perpendicularly. A Gaussian fit to this count profile provides an estimate for the FWHM of the myocardial wall. • To investigate the effects of noise, the frequency content of an image can be visualized by summing the Fast Fourier Transforms of 1-D radial profiles ofthe image. • To assist in evaluating the quality of images, a tool allows two images to be displayed simultaneously, either in their original scales or normalized to each other. In addition, images can be directly compared to other image of a similar size, by subtraction. In the case of computer simulations, where the true counts originating within each voxel is known, this tool can be used to compare an image with the corresponding true distribution of activity in the object. As mentioned, ImageTools software was used to quantitatively evaluate the spatial resolution, statistical noise and image artefacts of myocardial perfusion studies reconstructed using different techniques [200]. For this analysis patient, physical phantom and computer simulation images were used. It was shown that reconstructions that included AC and DRC, produced images with better spatial resolution and statistical noise, and less artefacts than other reconstruction techniques. Scatter correction was not included in this analysis. The aim of this thesis however was to assess the clinical impact of including physics-based corrections in SPECT reconstruction techniques. Although spatial resolution, statistical noise and image Chapter 4: Methods - Software Design 61 artefacts affect the accuracy of clinical information provided by nuclear medicine, other parameters more directly address the question of the clinical significance of SPECT corrections: the dosimetry of tumors, the size of myocardial perfusion infarcts, and the thickness of myocardial walls. Therefore new software was created to measure these clinical parameters. This new software additionally includes the original image analysis of ImageTools. The new software is called iQuant and includes functions entitled Dosimetry, Myocardial Quantitation and Liver Removal. Data sets are imported into iQuant in the same way as they are entered into ImageTools. The Dosimetry function allows tumors and other organs of interest to be delineated in 3-D and the activity originating within them measured. The Myocardial Quantitation function has two roles, the determination of myocardial perfusion infarct size (initial development [201]) and the measurement of myocardial wall thickness. The final function, Liver Removal, was not added to aid quantitation but to visually enhance clinical myocardial perfusion images. It outputs data sets from which the activity originating in the liver or other overlying organs has been removed. The three functions are all based on variations of the same 4 steps, each step being depicted by its own GUI, or window. The first step is the set-up window that allows the user to collect information specific to the data set; the central coordinates of the area of interest and if required, the maximum count in the organ of interest. The second step is the threshold window that specifies how an image is viewed subsequently; in its original linear colour scale, or on a stepped scale with specific thresholds or boundary conditions preset between colours. The third step is the display window which is the most complex. Here volumes of interest (VOI) are drawn, expanded, reduced, saved and erased. The final step is the calculation window where VOIs are subtracted from each other or from images, and VOI parameters are calculated. An addition tool allows the interpolation of 3-D matrices onto a new matrix 2 3 times as large, for example a 128 x 128 x 128 matrix interpolated onto a 256 x 256 x 256 matrix. Interpolations can be performed linearly or cubically. 4.2 iQuant - Dos imet ry For dosimetry, the distribution of activity within the body must be found as accurately as possible. This biodistribution of activity is measured from nuclear medicine acquisitions. Planar images in 2-D are simple to analyse, but 3-D VOI are necessary for accurate analysis of data sets produced from SPECT acquisitions. The 3-D process is complex. VOI should be coherent in all three dimensions, and it is not possible, by using standard software, to view the entire data set concurrently. The iQuant software is therefore an ideal platform to adapt to this task. The Dosimetry function is based on a simple principle, a VOI is drawn around the tumor and the total number of counts originating in the VOI is calculated, the tumor VOI is defined as voxels with counts greater than twice that of the mean background count (the reasoning behind this definition is explained in section 5.1.1.1 Biodistribution Calculations - Planar data - Simple method). Therefore a Chapter 4: Methods - Software Design 62 background VOI must be defined first. In this work the word 'tumor' is used to define any region for which dosimetry is required, this may be a tumor, but may also be a source organ (where the majority of the activity is located), or a critical organ (where dose must remain below a certain level because radiation damage could be dangerous to the patient). If the 'tumor' does not contain counts that are twice that of the mean background count (e.g. for a critical organ or a previously treated tumor), then a suitable VOI can be drawn by hand. 4.2.1 The method of Dosimetry In iQuant the user selects the data set of interest and the Dosimetry function is then initiated. The set-up window displays two slices of the data set, each showing a different dimension, for example an (x,y) image with a slice number in the z dimension, and an (x,z) image with a slice number in the y dimension (Figure 4.1). When the mouse is clicked on an image the program takes the coordinates of that point on the image (x^y,) and uses the number of the slice displayed to provide the third dimension (x-i.yLZi). The second image then changes to display the slice number, and a cursor specifies the position of (x,,zi). In this way any point in the 3-D data set can be located on both images. In the Dosimetry function the user specifies a point at the centre of the area of interest, initially a background region, and its coordinate is recorded by the program. This coordinate is used in subsequent analysis as a starting point for all display related activities. Title: thor_sc X coord: ("64" Y cooitfc [80 Z coord: [zb Third Dim Save coordinates of background or tumor 0 10 fl) L , „.,3P 0 SO 60 70 1 \* V . cond Dim. iQuant Figure 4.1: Set-up window of the Dosimetry function in iQuant, showing the cursors positioned in the centre of the tumor. Chapter 4: Methods - Software Design 63 As the background VOI is to be drawn first, the threshold window is used to display the images in their original linear scaling, with no threshold applied. In the display window the user draws a VOI of a sizable background region. Tools allow VOIs to be drawn, erased, added to, or reduced, across all slices or just in the displayed (or working) slice. Drawing can be done as a region (by specifying the apexes of a polygon, rectangle or oval) or as individual voxels. The user can use any slice in each of the dimensions as a "working image". Thumbnail images display the two alternative dimensions and indicate the slice presently displayed as the working image. The user can display a 3-D surface rendering of the VOI under construction and rotate it to view any angle (this is more useful when drawing the tumor VOI). Once the user is satisfied with the background VOI in every dimension, the VOI is saved and its parameters calculated. The mean count found within the background VOI is displayed and the Dosimetry function exited. To produce the tumor VOI the Dosimetry function is again initiated with the original data set, and the coordinate corresponding to the centre of the tumor is saved in the set-up window. In the threshold window the user enters a value of 2 times the mean background count. This will be used to find the boundary of the tumor. An "outline boundary" is also defined at a value of 1.5 times the mean background count. Once these parameters are applied to the data set, the subsequent images display every voxel with counts greater than the tumor boundary condition in red, every voxel with counts between the outline and tumor boundaries in green, and every other voxel in blue. In the display window the user can automatically select all voxels in red (with counts above the tumor boundary condition) as belonging to one VOI. The user can then flip through the data slices in all dimensions, removing any sections of the VOI that, in his opinion, are not associated with the tumor in question. Here the ability to produce a surface rendering of the VOI (Figure 4.2) directs the identification of unwanted VOI voxels. Once the VOI is satisfactory, it is saved and its parameters calculated. For dosimetry purposes the total number of counts in the VOI and its volume are displayed. Other VOI parameters displayed are mean counts, number of voxels, standard deviation of counts, maximum count, minimum count, and the dimensions of the complete data set. Figure 4.2: A 3-D surface rendering of a tumor VOI. Chapter 4: Methods - Software Design 64 Full instructions for operating the Dosimetry section of iQuant can be found in Appendix B1. 4.3 iQuant - Myocardial quantitation The development of the iQuant software for quantitation of myocardial perfusion infarct size was originally motivated by a clinical request for accurate in-house measurement of data sets from a research clinical trial. Available commercial software programs (discussed in section 2.4.2.5 Methods used for the evaluation of myocardial detect size) rely upon the creation of polar maps and the comparison of each data set to a database of normal scans. This database is created for the specific camera, acquisition protocol, collimator, patient gender, body habitus, SPECT reconstruction technique, applied corrections, spatial filter, etc and therefore many databases are required, each containing data sets from a substantial number of normal patients. Within iQuant it is possible to measure infarct size, working completely in 3-D (therefore not relying on a polar map approximation), and independently of a normal heart database. The iQuant Myocardial Quantitation function measures infarct size based on the following principles. Infarct size is traditionally measured as a percentage of the total LV myocardial volume. In order to do this it is necessary to evaluate the total size of the myocardium (viable and infarcted tissue) and to measure the size of the infarct itself (a region of the myocardium showing significantly less uptake of tracer than the viable tissue). A result can therefore be obtained by drawing two VOI, one containing only the viable LV tissue, and the other containing the entire LV myocardium (viable tissue plus infarct). The final result is the difference in size between the two VOI divided by the size of the entire LV VOI. The iQuant Myocardial Quantitation function also measures myocardial wall thickness. Although the drawing of a VOI is not necessary for the measurement of wall thickness, multiple boundary conditions can be applied to the displayed data set to determine the position of the epi- and endo-cardiac surfaces (the surfaces between which the wall thickness is measured). Thickness measurements are performed on the anterior, lateral, inferior and septal walls of the LV from three representative short axis slices. 4.3.1 The method of Myocardial quantitation For measurements of both myocardial infarct size and myocardial wall thickness, the relevant reorientated cardiac data set is read into iQuant. In the set-up window the user positions the cursor in the centre of the LV and saves the coordinates of that point (Figure 4.3). This coordinate will be used as a starting point in the next stages of the analysis. The user then moves the cursor to a point within the LV myocardium itself. From this point a region is automatically grown, initially using voxels containing 50% of the maximum voxel counts in the entire data set as the stopping criteria. A 3-D surface rendering of the region is displayed. This 3-D image can be rotated and viewed from any angle. The information obtained from this region is the mean value of the 30 voxels showing maximum counts in the LV myocardium. Therefore, if the region is small and contains less than 30 voxels, or if the region is too big and contains voxels that are outside the LV (e.g. liver voxels), then the region must be re-grown with the Chapter 4: Methods - Software Design 65 user specifying a smaller or larger stopping criteria as required, see Figure 4.4 and 4.5. Once the user is satisfied that the region contains a sizable portion of the LV only, the mean value of the maximum 30 voxels is calculated and saved by the program. i Title: r9r_wall_pat_sc Check list: X coord: [IT Y coord: ["IT Save coordinates of cardiac center | Done Z coord: I if s Find max count in cardiac | • , , Second C Hafrtsh Colorbar Figure 4.3: The set-up window of the Myocardial Quantitation function in iQuant, showing the cursors positioned in the centre of the left ventricle. Figure 4.4: A 3-D surface rendering of a region grown from a point in the myocardium. Using 50% of the maximum voxel counts in the entire data set as the stopping criteria, the myocardium and the close lying liver have been included in the region. Chapter 4: Methods - Software Design Figure 4.5: A 3-D surface rendering of a region grown from a point in the myocardium. Using 60% of the maximum voxel counts in the entire data set as the stopping criteria, only the LV myocardium has been included in the region. This mean value of the maximum 30 voxels is displayed in the threshold window and the subsequent boundary conditions (thresholds) will be defined as a percentage of this value. The threshold used to define the viable myocardial tissue depends upon the technique used to reconstruct the data set. The method used to determine these thresholds is detailed in section 5.3.1.1 iQuant -Boundary condition thresholds and the results of the subsequent analysis is detailed in section 6.3.1 Software Validation - Boundary condition thresholds. A lower threshold is also defined to aid the user when the extent of the myocardial infarct is being determined. This outline threshold is set at the discretion of the user, but a rule of thumb places it at a value of 15% to 20% below the viable threshold. The outline threshold is not relevant to the measurement of myocardial wall thickness. When the image is displayed all voxels with counts greater than the threshold used to define the viable myocardial tissue, are shown in red. All voxels with counts between the two thresholds are shown in green, and all other voxels in blue. In the display window the methods used to determine myocardial wall thickness and myocardial infarct size vary. The former will be described first. The user selects the short axis view of the LV and using the coordinates saved earlier in the program, the central slice of the LV is displayed. The thickness of the central section of the anterior, lateral, inferior and septal LV walls is measured by counting the number of red voxels across each wall (Figure 4.6). To aid this measurement a VOI can be automatically drawn that contains all voxels displayed in red. By starting the tool designed to add or remove individual voxels from a VOI, an image is displayed in which all VOI voxels contain an orange dot. Also, in this mode, the cursor is displayed as a vertical cross with vertices that extend out to the edge of the image. Therefore, if the user places the cursor in the centre of the LV, its vertices will lie across the centre of each myocardial wall. The thickness of each wall corresponds to the number of orange dots that lie along the centre of that wall. Once these four measurement have been recorded, the tool is deactivated. Chapter 4: Methods - Software Design 67 Anterior wall Position of cursor Lateral wall thickness thickness Figure 4.6: The position of wall thickness measurements taken from a short axis slice of the LV myocardium. Similar wall thickness measurements are taken from two additional short axis slices, the first, three slices closer to the LV apex, and the second, three slices closer to the LV base. If wall thickness measurements are required using a different boundary criteria (which occurs in the investigations described in subsequent chapters), then the user can return to the threshold window and reset the viable threshold. The use of the display window to determine myocardial infarct size is more dependent upon the operator (Figure 4.7). Firstly a VOI is automatically drawn which includes all voxels containing counts above the viable threshold (all those displayed in red). The user then flips through slices in all three dimensions, removing any voxels that are not within the LV myocardium. Usually liver and RV voxels will need to be removed. A 3-D surface rendering of the VOI under construction can be viewed at any time. This is used to determine the location of unwanted VOI voxels, and eventually to view the completed viable LV VOI. Once the user is satisfied with the VOI, it is saved and also remains active as the next VOI simply adds to the first one. Using the 3-D surface rendering of the viable LV VOI, or 2-D cross-sectional slices, areas of myocardial infarct are identified. As an infarct usually contains a higher concentration of radiotracer than background tissue (therefore more than the lower threshold) but significantly less that viable myocardium (therefore less than the higher threshold) [115], the outline ofthe wall containing the infarct will be indicated by the green voxels. The thickness of the wall containing the infarct can be estimated by comparing it with healthy sections of the myocardium. These two indications together with knowledge of myocardial physiology and anatomy, are used to add the infarct onto the existing VOI. Every slice containing the infarct is viewed in every dimension to ensure the resulting VOI is smooth (like the myocardial surface) and represents the entire LV myocardium. The 3-D surface rendering tool is again Chapter 4: Methods - Software Design 68 useful in viewing the VOI. Once the complete LV VOI is acceptable, it is saved. A pictorial representation of this method is presented in Figure 4.8. Auto Select VOI J Apply to All il Draw Area Erase Area Remove Exterior Clear Selection Add/Re move Voxels 1 Zoom Save Liver Save B/G Dimension Find Pixel Value Previous: Finished ept/Change Thresholds ^3 Figure 4.7: The display window of the Myocardial Quantitation function in iQuant, showing a short axis slice of the myocardium and close lying liver. In the calculation window, from a list of all the saved VOIs in chronological order, the correct viable and complete LV VOIs are selected. The infarct size is then calculated and information pertaining to the infarct is displayed. This information includes the size of the infarct as a percentage of the complete LV, the volume ofthe infarct in voxels and ml, the standard deviation of counts found within the infarct, and the mean, total, maximum and minimum of these counts. A surface rendering of the composite VOI is also presented with the viable tissue displayed in brown and the infarct in green. Full instructions for operating the Myocardial Quantitation section of iQuant can be found in Appendix B2. The first version of the iQuant method of myocardial infarct size measurement was presented at the Canadian Organization of Medical Physics Annual Meeting 2003 [202] and at the IEEE Medical Imaging Conference 2003 [203]. Chapter 4: Methods - Software Design 69 a) Slices of static MCAT phantom with lateral infarct b) The three-tone image is created using the viable and outline thresholds as the transition between the colour bands l iable threshold Outline threshold c) The viable threshold is used to define viable LV VOI r, c d) The outline threshold and the thickness of the viable myocardium is used by the operator to assist in the "filling-in" of the infarct o e) The complete LV VOI o Figure 4.8: The steps involved in iQuant to determine the viable and complete LV VOIs of a data set from the static MCAT phantom with an infarct in the lateral wall. Steps are depicted for a horizontal long axis slice (left hand column), and a short axis slice (right hand column). Chapter 4: Methods - Software Design 70 Additional features of iQuant that ensure its suitability as a research tool include the ability to save VOI into the external workspace, to load VOI from the external workspace into iQuant and apply them to different data sets, the ability to change colour scales and maps, and to deal with data sets that are not of a uniform size. Further information on these tools can be found in Appendix B3 Additional general instructions for iQuant. The experiments used to evaluate the accuracy and reliability of the present version of iQuant in its determination of myocardial infarct size are described in section 3.3.3 Software validation and 5.3.1 iQuant, and the results are presented in section 6.3.2 iQuant accuracy and section 6.3.3 iQuant reliability. 4.4 iQuant - Removal o f over ly ing l iver f r o m myocard ia l images As discussed earlier, excessive isotope uptake in the liver, gall bladder, small and large bowel, or stomach, all of which lie close to or overlying the myocardium, interferes with the visualization of the inferior myocardial wall. For simplicity in the remainder of this work, all of these organs shall be referred to as the liver. The Liver Removal function in iQuant is designed to provide a clinical tool to allow cardiologists a clearer view of myocardial perfusion images. This is particularly important for reconstructions including AC, DRC and SC as they enhance the visibility of organs lying close to the myocardium. Therefore the tool is designed to assist the diagnosis by removing the activity from these regions in the images and replacing it with background activity. It does not however remove the activity originating in the liver but scattering in the myocardium and hence appearing to originate in the myocardium. 4.4.1 The method of Liver removal As for all other functions, a data set is read into iQuant. The Liver Removal function is then initiated. In the set-up window a point in the centre of the LV is selected and its coordinates saved. Next, a voxel within the LV myocardium is selected and a region is grown from this point providing a rough outline of the LV. The initial stopping criterion is 50% of the maximum voxel count in the entire data set, but this can be changed if it is unsuitable, for example if the resultant region contains voxels outside the LV. The final estimate of this region provides a value for the mean value of the maximum 30 voxels in the myocardium, as for the Myocardial Quantitation function. This value is used when setting the boundary conditions for the subsequent data set display. In the threshold window default boundary condition values are displayed; 50% for the myocardium and 20% for the surrounding increased activity which will include the liver and possibly the right ventricle. In subsequent images all voxels containing counts above 50% of the maximum myocardial count are displayed in red, all voxels with counts of between 20% and 5 0 % are green, and all other voxels are blue. In the display window the user draws a VOI containing background voxels, the count from which will eventually replace the liver volume. The background VOI is saved. A new VOI then is automatically Chapter 4: Methods - Software Design 71 drawn around all voxels which contain counts greater the lower 20% threshold (all red and green voxels). The user removes the LV from this VOI, but leaves in any right ventricle (RV) activity and the extra-cardiac activity of the liver. Once the VOI is satisfactory, it is saved. In the calculation window the background and liver VOIs are selected and, at the click of a button, the counts from liver VOI are removed from the data set and replaced by the mean counts from the background VOI. Two images of the central short axis slice of the myocardium are displayed, one in its original form and one with the liver activity removed (Figure 4.9). Any short axis slice can then be displayed. If the user is satisfied with the resultant images, the data set is saved to the MATLAB workspace and also to the present working directory on the hard drive. Choose the Liver VOI Liver VOI1 Choose the Background VOI B/G VOI2 - I Remove Liver Original Data; Liver VOI info Background VOI Info Mean:2.2284 Mean 0 55671 Number of Voxels: 19358 1 Standard Deviation: 1.8614 s Maximum Value: 7.9354 1 Minimum Value: -0.054526 Volume: 2134.1568 ml Dimensions: 128 x 128 x 38 I Number of Voxels: 2528 Standard Deviation: 0.29423 Maximum Value: 2.0689 Minimum Vakje: 0,053176 Volume; 278.7038 ml Dimensions: 128 x 128x38 Data with Liver Removed: Next Slice Figure 4.9: The calculation window of the Liver Removal function in iQuant, showing a short axis image of the original data set (left) and the same image with the liver removed (right). Full operating instructions for the Liver Removal section of iQuant can be found in Appendix B4. 72 C H A P T E R 5 M E T H O D S - Q U A N T I T A T I V E M E A S U R E M E N T 5.1 Dos imet ry 5.1.1 Biodistribution calculations Biodistribution calculations were carried out on all dosimetry acquisitions to estimate the activity situated in the tumor at a given time. For planar acquisitions (static or whole body) two calculation methods were applied, one very simple and the other more complex, but both requiring the manual drawing of regions of interest (2-D) around the tumor on the images. For SPECT acquisitions the calculation itself was simple, but the drawing of the volume of interest (3-D) on the data set was more complex and required the use of the iQuant software. 5.1.1.1 Planar data - Simple method The simplest and quickest method to estimate the activity within a tumor from planar acquisitions is to calculate the mean value of these images. This method is carried out routinely in many clinical centres and relies on numerous assumptions and approximations. It was performed here to determine the extent of its inaccuracies. The method can be performed using the arithmetic or geometric mean of the two planar images, and both were calculated here to allow for comparison. The arithmetic mean (PA„) of anterior (/„) and posterior (lP) images was calculated using the maximum thickness of the body (f), and the linear attenuation coefficient of water (//): PGeo = -JUAJP) e X P (5.1) (5.2) p - ( / ' + / 'W^l rAri 0 C X P n I \ 2 J The geometric mean (PG e o) of these images was calculated using the following formula: 'EL) 2 , Regions of interest (ROI) were drawn around the tumors on these two mean images. For the simple simulation study (section 3.12 Simple 2-D simulation) of one slice of the body, which did not model collimator blurring, the 'image' was 1-D, and the ROI corresponded to the four pixels encompassing the tumor area. For the 3-D computer simulations and phantom experiments, the ROI was defined as the 2-D region around the tumor that contained counts greater than twice the mean background count. Therefore a Chapter 5: Methods - Quantitative Measurement 73 large background ROI was drawn first, allowing the calculation of the mean background count in the image. The tumor ROI boundary and the volume of interest (VOI) boundaries in the subsequent sections, were defined using background counts and not tumor counts. This was done as the background activity level shows less statistical variation and less variation between patients than the tumor activity uptake. Two methods are commonly used for the definition of ROI boundaries as a function of background counts: (1) the area containing counts greater than twice that of the mean background count, and (2) the area containing counts greater than the mean background count plus twice its standard deviation. This latter method however, when used in the iQuant analysis, repeatedly provided an ROI whose geometry did not match that of the tumor. The former method consistently provided an ROI centred on the known tumor site with a similar geometry and was hence chosen for these experiments. To provide an estimate of the absolute activity localized within the tumor (AE), the total number of counts originating within the ROI was corrected for the sensitivity of the system. For the 2D simulation study, the sensitivity of the system was not included in the simulations, therefore the counts originating within an ROI were directly equivalent to the activity estimate. 5.1.1.2 Planar data - Complex method The more complex and comprehensive method for dosimetry calculations based on information from planar projections is described in the MIRD Pamphlet 16 [204]. It is designed to correct for background activity, self-attenuation of the tumor and attenuation through the slice. An ROI was drawn around the tumor on both the anterior and posterior images using the methods described in the previous section. The count rate from these ROIs were measured, RA and RP, respectively. Using the sensitivity of the system C (referred to as the system calibration factor by MIRD), the estimated activity, Aj, of a tumor (J) was calculated: where t is the maximum thickness of the body, p is the linear attenuation coefficient of water, f, is the correction for the thickness of the tumor, and F is the fraction of the geometric mean of the counts that originated in the tumor itself. These last two factors are defined in equations 5.4 and 5.5, with f; as the thickness of the tumour (measured from a lateral projection of the body), ps as the attenuation coefficient of the tumor, and RADJ as the count rate from a background ROI adjacent to the tumor ROI and equal to it in area. (5.3) f V 2 (5.4) sinh V 2 J Chapter 5: Methods - Quantitative Measurement 74 F = R ADJ R A A RADJ V RP J t (5.5) J 5.1.1.3 SPECT data Reconstructed SPECT data sets were analysed using the Dosimetry section of the iQuant software as described in section 4.2 iQuant - Dosimetry. In brief the method initially involved the drawing of a 3-D VOI of background activity. As for the tumour ROI in the previous section, twice the mean count value in the background VOI was used to define the boundary condition of the tumor VOI. The iQuant software outputs a surface rendering of the tumor VOI and a list of parameters including the total number of counts originating within it. This number was then divided by the system sensitivity to give an estimate of the activity originating within the tumor. Correct normalization of the reconstruction algorithm was required. 5.1.2 System sensitivity measurement To calculate the system sensitivity C of the simulated and true gamma cameras, a static planar acquisition was performed of a point source in air for each system. The counts registered in every pixel of each camera head (2 heads for the gamma camera and 1 for the computer simulation), were summed to give the total number of counts accepted by the camera during the scan time. To calculate the system sensitivity, the total number of counts accepted was divided by the total time length of the scan (in minutes) and by the activity of the point source placed in the camera's field of view at the time of acquisition. This provided a value of the system sensitivity measured as the number of counts acquired per minute of scan time per kBq of activity (counts/min/kBq). 5.1.3 Activity decay To calculate the accuracy of the activity estimates measured from the phantom experiments, knowledge of the activity in the phantom at the time of acquisition was required. The activity within the tumor (AT) at the time (f) each scan was acquired, was calculated using the exponential relationship between activity and time, the initial administered activity {A0) and the half-life of 9 9 m T c (T1/2=6.02 hr): j —/it - In 2 Aj = A0e where: A = (5.6) Tl/2 Chapter 5: Methods - Quantitative Measurement 75 5.1.4 Comparison to the truth Each study was carried out in a controlled situation where the true activity originating within the tumor was known. Therefore, a relative difference could be calculated between the experimentally determined activity estimate (AE) and the truth (AT): Relative Difference r A - A ^ x 1 0 0 (5.7) For each situation the experimental error in AE was estimated. For the physical phantom an additional error was incurred in the measurement of AT. These experimental errors are described throughout section 6.1 Results and Discussion: Dosimetry and were used to provide an absolute error for each result presented. 5.1.5 Statistical analysis Throughout this work SPSS software version 11.0 was used for the statistical analysis of data. The relative difference between the estimated and true tumour activity for each tumour, acquisition and reconstruction technique, was compared. Data from different acquisitions were compared using independent-sample t-tests, with a significant difference between the two groups being presumed for values of p<0.05. Paired-sample t-tests (p=0.05) were used to compare different reconstructions or biodistribution calculations of the same acquisition data sets. For a paired-sample t-test the difference Dh...Dn is found between data X,,...X„ from one set of reconstructions and data Y1: ...Y„from a second set of reconstructions of the same acquisitions: Di=Xi-Yi (5.8) The parameters D , Sd and n are the mean, standard deviation and size of this new sample. The paired-sample test statistic (7) is then described by the following equation: Sd Nn An independent-sample t-test can be used to compare data Xx...Xnx reconstructed from one set of acquisitions and data Yx --Yn^ reconstructed from a second set of acquisitions. The parameters X, S\ and nx, and Y , Sy and nyare the mean, variance and size of the two samples, respectively. Chapter 5: Methods - Quantitative Measurement 76 (5.10) The independent-sample test statistic (7) is then described by the following equations: T X-Y (5.11) + 5.2 Myocard ia l Wal l Th ickness Myocardial wall thickness was measured using the Myocardial Quantitation section of iQuant, as described in section 4.3 iQuant - Myocardial Quantitation. Viable myocardium thresholds were varied, in 5% intervals, from 40% to 75% of the maximum myocardial count determined over 30 voxels. Measurements of myocardial wall thickness were made for each of these thresholds where possible. During this process, for each data set and each threshold, observations were made about the appearance of the LV myocardium. Observations included the appearance of holes in the myocardium, and for the clinical data sets, the difference in length between opposite myocardial walls, and the presence of RV tissue or liver tissue with counts greater than the threshold. The 12 measurements taken of myocardial wall thickness (1 measurement across each of the four walls of 3 short axis slices), corresponding to each threshold (j) of each data set (/), were averaged to give a mean value, m^. To produce graphical representations of the results, for a given threshold, all values of m,y for data sets adhering to a given set of parameters (k), were averaged to give Mjk. For example, the average myocardial wall thickness was calculated of all data sets from phantom experiments which were reconstructed using OSEM+AC+DRC+SC. These values were presented with their Confidence Intervals (Cl) to graphically show the range of values that have a 95% chance of containing the average wall thickness of the entire population. A mean value, M, with a standard deviation of crfrom n samples, and a Cl of 95%, can be written with its Cl limits [205]: mean ± 1.96 (5.12) Chapter 5: Methods - Quantitative Measurement 77 5.2.1 Statistical analysis The mean values (m,y) of the myocardial wall thickness measurements were analysed. Dependent variables (e.g. different reconstructions of the same acquisition data set), were compared using the paired-sample t-tests, with a significant difference between the two groups being presumed for values of p<0.05. Independent variables (e.g. results originating from independent acquisitions), were compared using the independent-sample t-tests, with no significant difference found between groups for values of p>0.05. In order to determine the number of clinical cases that should be used in this analysis, power calculations were carried out prior to the collection and analysis of the complete clinical database [206]. This value of power gives the probability that if an effect is present, it will be observed in the data. From preliminary data sets (a database of 16 patients with <5% likelihood of CAD), it was noted that the difference in wall thickness m,,, determined using consecutive thresholds, was approximately constant and averaged 0.42 voxels (voxel dimension 4.8 mm). It was therefore decided that this difference of 0.42 voxels be considered significant in statistical tests as the difference between the mean of two populations {Mjkm - Mjk(2j). The standard deviation of the population was also found from the preliminary data sets as u = 0.46 (the standard deviation of all m,y values for a given threshold). The effect size, d, for the power calculations was then found: d = M y * ( 1 ) ~ M y * ( 2 ) = 0.913 voxels (5.13) CT Each statistical test applied to the clinical database would be 2-tailed with a Type I error of a = 0.05 (standard for investigations of clinical data sets). As multiple comparisons would be performed on the database, the critical a for the group was transformed to <0.01 by the Bonferroni adjustment [207]: . . . individuala critical a = (5.14) # comparisons The value of a used for the power calculations was therefore 0.01. Clinical research should be carried out with a power of equal to or greater than 80% [207]. For the paired-sample t-test, a power of 0.8 (or 80%) would be achieved from 18 data sets in each group. For an independent-sample t-test, a power of 0.8 would require 31 data sets per group. Power calculations are not relevant for computer simulation and physical phantom experiments, as the standard deviation of the population is zero giving an infinite effect size. Chapter 5: Methods - Quantitative Measurement 78 5.3 Myocardial Infarct Size Myocardial infarct size was measured using the Myocardial Quantitation section of iQuant, as described in section 4.3 iQuant - Myocardial Quantitation. 5.3.1 iQuant 5.3.1.1 Boundary condition thresholds Boundary conditions (thresholds) used for iQuant infarct size measurements were derived from analysis of the computer simulation and physical phantom acquisitions. For each position, size and severity of infarct, iQuant measurements were taken of infarct size from 3 (of the 5) reorientated data sets. Each measurement was repeated for a set of thresholds, varying in 5% steps from 35% to 75% of the maximum myocardial count. The threshold that provided the most consistently accurate measure of infarct size for each position, size and severity of infarct, is detailed in section 6.3.1 Boundary condition thresholds. 5.3.1.2 Accuracy To determine the accuracy of the iQuant technique in measuring myocardial infarct size for patient studies, infarct size measurements were taken of the original MCAT phantom with a beating heart (with no SimSET simulations). Each of the 4 phantoms, containing a medium sized infarct in a different myocardial wall, was measured a total of 4 times on separate occasions by the same observer. The absolute error between the true infarct size (averaged over time) and the average value measured with iQuant was calculated for each infarct location, and then averaged for all locations. 5.3.1.3 Reliability To determine the reliability of the iQuant method, three independent observers performed infarct size measurements using the 5 repeated phantom acquisitions detailed in section 3.3.3 Software validation. Each observer analysed each of the five studies on separate days. From these measurements both inter- and intra-observer reliability was determined. In this case the intra-observer variation is the variance within the measurements of one observer, calculated across all three observers. The inter-observer reliability coefficient (R) is the correlation coefficient found when two observers measure the same target. It is based on the analysis of variance (ANOVA) and contains terms for the variance of the target (ae 2) and the variance of the observer or rater (aR 2): Chapter 5: Methods - Quantitative Measurement 79 The reliability coefficient formula had to be altered from its standard format to take into account the measurements of three observers (the standard formula is set up to take the measurements of only two observers), measuring the same repeated target [207]. 5.3.1.4 Comparison with other myocardial quantitation programs For the comparison of iQuant with the Mayo Clinic software program, the phantom data sets were reconstructed using FBP (as no transmission data were acquired). Myocardial infarct size measurements determined from iQuant and from the Mayo Clinic, were compared to the true infarct size using linear regression analysis. For the comparison of iQuant with 4D-MSPECT [148] [156], the 22 clinical myocardial perfusion studies from patients with a recent Ml, were reconstructed with FBP. Additionally, the 13 of these studies that included transmission acquisitions were reconstructed using OSEM+AC+DRC. The myocardial infarct size of each data set was measured with both iQuant and 4D-MSPECT. 4D-MSPECT works by comparing polar maps derived from the mid-myocardial surface, to a database of normal hearts. For use in this study it was adapted to use thresholds instead of normal heart databases. This was possible as the author of the software, Prof. E. Ficaro, provided a series of 5 uniform polar maps, which when implemented allowed thresholds of 40%, 45%, 50%, 55% and 60% to be applied to new patient data sets. 5.3.2 Statistical analysis In the analysis of data sets acquired from the myocardial infarct size computer simulations and phantom experiments, linear regression analysis was used to determine the relationship between the true size of the infarct and that measured from the reconstructed data sets. Graphs composed of 15 measurements of 3 different infarct sizes investigated this relationship for each location of infarct and each reconstruction technique. The slope of the linear regression line (b) represented the relationship between the measured infarct sizes and the true values, with a slope of 1.0 representing completely accurate set of measurements. The error of slope (se(b)) indicated how well these 15 measurements clustered around the regression line, with a low error showing results consistently close to the line. For these experiments the intercept of the regression line with the x or y axis was not critical as infarcts of very small sizes are not considered clinically relevant. To compare the slopes (bj and b2) of regression analysis performed on two sets of measurements, the null hypothesis was set: It is presumed that the true slope of the first set of measurements is equal to that of the second set of measurements. H0 : fa = fa. It is also assumed that the slope (b) of the regression line is an estimation of the true slope (fa for each set of measurements. Chapter 5: Methods - Quantitative Measurement 80 If the distribution is normal, and if the slopes are significantly different with p=0.05, then the value of equation 5.16 will be greater than the critical value of 1.96. However, 6 comparisons were drawn between the data sets of each reconstruction technique and therefore, using the Bonferroni adjustment (discussed in section 5.2.1 Myocardial wall thickness -Statistical analysis), the value of p was reduced by a factor of 6 to 0.0083. The critical value in equation 5.16 was adjusted to 2.64 to comply with smaller p value [207]. Additionally, each linear regression slope was compared to the ideal value of 1. In this situation equation 5.16 simplified to equation 5.17, with the number of comparisons remaining at 6 and therefore a critical value of 2.64. > 1 . 9 6 (5.16) 6 , - 1 > 2 . 6 4 (5.17) se(bx) The effect of infarct location on the accuracy of the reconstruction of infarct size, was determined by calculating the absolute error of the measurement averaged over the different infarct sizes for each location. 81 C H A P T E R 6 R E S U L T S A N D D I S C U S S I O N 6.1 Dos imet ry 6.1.1 Simple 2-D simulation The simple 2-D simulation was designed to indicate the error arising from biodistribution information gathered from planar acquisitions and simple calculations. The relative difference between the estimated tumor activities and the true tumor activities are displayed in Table 6.1 (see section 5.1.4 Comparison to the truth for the definition of relative difference). Due to the simple nature of these simulations there were no experimental errors in the measurements; distances were known exactly and as there was no simulation of photon scatter, ROIs were drawn precisely over the tumor site. Therefore the results are presented without errors. Table 6.1: Relative difference between the true tumor activity and that estimated from the arithmetic and geometric means of planar acquisitions derived from the 2-D simulation. Tumor to background activity ratio Tumor location Relative difference between the estimated tumor activity and the truth (%) Arithmetic mean Geometric mean 6:1 A -14.14 -14.14 B -32.79 -24.91 C -80.77 -80.77 D -26.67 -26.67 E -32.11 -29.71 1:0 A -6.44 -6.44 B -34.08 -6.44 C -71.43 -71.43 D -8.70 -8.70 E -19.89 -8.70 Chapter 6: Results and Discussion 82 6.1.2 Comprehensive simulation The more comprehensive MCAT and SimSET simulations were performed to compare methods of activity estimation based on planar and tomographic acquisitions. For the SimSET parameters used in this more comprehensive simulation, the system sensitivity was 4.08 counts/min/kBq. The values of tumor activity estimated from planar acquisitions using the simple and complex calculations and from SPECT acquisitions reconstructed using OSEM+AC+DRC are displayed in Table 6.2. For the planar data sets, the error values presented in this table were associated with the defining of the tumor and background ROIs. The 2% error in the defining of the background ROI (experimentally measured from 6 repeated ROIs), also affected the defining of the tumor ROI by a maximum of 2%. The system sensitivity, and phantom and tumor thickness were known exactly and therefore no errors were associated with their measurement. When these errors were included into the simple biodistribution calculations for planar data sets (detailed in section 5.1.1.1 Planar data - Simple method), the resultant experimental error in the estimation of tumor activity was 2.5% for the arithmetic mean and 2.0% for the geometric mean. For the complex biodistribution calculations (detailed in section 5.1.1.2 Planar data -Complex method), the resultant experimental error in estimated tumor activity was approximately 4%. For SPECT data sets, the error values were associated with the defining of the tumor VOI. Again resultant on the defining of the background VOI, and now in 3-dimensions, the error value for the total counts originating in the tumor VOI was 4% (experimentally determined from 6 repeated VOI measurements). As the estimate of tumor activity derived from SPECT data sets simply requires the total number of counts in the tumor VOI to be divided by the system sensitivity, the experimental error of the activity estimate remained 4%. Table 6.2: Tumor activity estimated from planar and SPECT acquisitions of the thorax simulation. Estimated tumor activity (kBq) True Planar Planar Planar SPECT Tumor tumor Simple Simple Complex OSEM+AC+DRC Tumor volume activity arithmetic geometric calculation reconstruction location (ml) (kBq) calculation calculation Abdomen 34 8677 13759 ±344 11995 ±240 8212 ±328 7508 ± 300 Lung surface 34 8677 15724 ±393 15396 ±308 12330 ±493 8881 ±355 The relative difference between the true tumor activity and the estimated activity is presented in Table 6.3. The errors displayed in this table were derived from the errors in the estimated tumor activity values. Chapter 6: Results and Discussion 83 Table 6.3: Relative difference between the true tumor activity and that estimated from planar and SPECT acquisitions of the thorax simulation. Tumor location Tumor volume (ml) Relative difference between true and estimated tumor activity (%) Planar Simple arithmetic calculation Planar Simple geometric calculation Planar Complex calculation SPECT OSEM+AC+DRC reconstruction Abdomen 34 58.6 ±4.0 38.2 ±2.8 -5.4 ±3 .8 -13.5 ±3.5 Lung surface 34 81.2 + 4.5 77.4 ± 3.5 42.1 ±5.7 2.4 ±4.1 6.1.3 Phantom experiments Physical phantom experiments were performed to compare tumor activity estimates resulting from the use of different SPECT reconstruction techniques. Additionally the data sets were used to compare the tumor activity estimates derived from static planar and whole body planar acquisitions. The comparison between static planar and whole body planar acquisitions is presented first. The total system sensitivity from the dual-headed gamma camera was measured as 11.1 ± 0.5 counts/min/kBq. The activity estimates of the Thorax tumors and the radioactive spheres of the Jaszczak phantom, resulting from static planar and whole body planar acquisitions, are presented in Table 6.4. Activity estimates of the two smallest spheres are not presented as it was not possible to differentiate them from background activity. Table 6.4: Tumor activity estimated from the complex calculations of static planar and whole body planar acquisitions of the Thorax and Jaszczak phantoms. Region under investigation Volume under investigation (ml) Static planar Whole body planar True activity (kBq) Estimated activity (kBq) True activity (kBq) Estimated activity (kBq) Thorax tumor Anterior spine 12 2682 ± 54 880 ± 70 2958 ± 59 768 ±61 Lung base 8 1731 ±35 1057 ± 8 5 1909 ± 3 8 1125 ±90 Jaszczak sphere 6 29 4459 ± 89 3851 ± 308 4724 ± 94 4911 ±393 5 16 2399 ±48 1846±148 2541 ± 51 2469±198 4 6 1192 ±24 1024 ±82 1263 ± 2 5 1047 ±84 3 3 4 1 9 ± 8 251 ± 2 0 443 ± 9 318 ±25 The error values presented in this table were derived from the same principles as the planar results collected from the computer simulations, but with the following additional factors. The measurement of Chapter 6: Results and Discussion 84 phantom thickness and tumor thickness, performed on a lateral image of the phantom, introduced experimental errors of 1% and 2% respectively. An error was also associated with the measurement of system sensitivity. The resultant experimental error in the estimation of tumor activity was approximately 8%. The relative difference between the true tumor or radioactive sphere activities and their estimated activities is presented in Table 6.5. The errors displayed in this table were derived from the errors in the estimated tumor activity values and the 2% error associated with the measurement of the true activity in a dose calibrator. Table 6.5: Relative difference between the true tumor and radioactive sphere activity and that estimated from static planar and whole body planar acquisitions ofthe Thorax and Jaszczak phantoms. Region under investigation Volume under investigation (ml) Relative difference between the estimated activity and truth (%) Static planar acquisition (kBq) Whole body acquisition (kBq) Thorax tumor Anterior spine 12 -67.2 + 4.6 -74.0 ±4.1 Lung base 8 -38.9 ±6.9 -41.1 ±6 .7 Jaszczak sphere 6 29 -13.6 ±8.9 4.0 + 10.3 5 16 -23.1 ±8.2 -2.8 ±9.8 4 6 -14.1 ±8.9 -17.1 ±8.6 3 3 -40.2 ± 6.8 -28.2 ± 7.8 Taking all tumors and radioactive spheres into account no significant difference was found between the measurements obtained from the static planar acquisitions and those from the whole body planar acquisitions (p>0.05 using an independent-sample t-test). However, the accuracy (determined using the relative difference parameter) of the estimates of tumor activity in the Thorax phantom are significantly different from those of the radioactive spheres of comparable size in the Jaszczak phantom (p=0.05). The measurements taken from the Thorax phantom with varying linear attenuation coefficients are consistently further from the truth than the measurements taken from the Jaszczak phantom with uniform attenuation properties. Chapter 6: Results and Discussion 85 The physical phantom experiments were then used to compare tumor activity estimates resulting from the use of different SPECT reconstruction techniques. The activity estimates of the Thorax tumors and the radioactive spheres of the Jaszczak phantom, resulting from different SPECT reconstruction techniques, are presented in Table 6.6. The error values presented with the results in this table were derived from the 4% error value of the total counts originating in the tumor VOI, and the error in the measurement of system sensitivity. The resultant experimental error in estimated tumor activity was approximately 6%. However, for the radioactive spheres in the Jaszczak phantom, VOIs (with boundaries defined as twice the mean background counts) required manual manipulation to separate them from neighbouring spheres or, in the case of data sets that were not attenuation corrected, from the outside surface of the phantom. This manual manipulation added an additional error estimated at 5%, resulting in an experimental error in estimated tumor activity for the Jaszczak phantom of approximately 11 %. Table 6.6: Tumor and radioactive sphere activity estimated from SPECT acquisitions of the Thorax and Jaszczak phantoms reconstructed with different techniques. Region (Volume, ml) True activity (kBq) Estimated activity (kBq) FBP OSEM OSEM+ DRC OSEM+ AC OSEM+ AC+DRC OSEM+AC +DRC+SC Thorax tumor Anterior spine (12) 2367 ±47 159 ±10 264 ±16 269 ±16 996 ±60 1818+109 2143 ±129 Lung base (8) 1528 ±31 74 ±4 80 ±5 109 ±7 590 +35 1151 ±69 1457 ±87 Jaszczak sphere 6(29) 3929 ±79 585 ±64 965 ±106 948 ±104 2483 ±273 3283 ±361 3729+417 5(16) 2113±42 347 ±38 545 ±60 517 ±57 1121 ±123 1657 ±182 1974+217 4(6) 1050 ±21 186 ±20 325 ±36 327 ±36 571 ±63 815+90 1004+110 3(3) 369 ±7 108 ±12 186 ±21 192 ±21 279 ±31 421 ±46 501 ±55 2(2) 235 ±5 53+6 94 ±10 104 ±11 100 ±11 186+20 280 +31 1 (1) 98 ±2 6±1 9±1 8±1 * * 48 ±5 * It was not possible to differentiate the smallest radioactive sphere from the background activity. The relative difference between the truth, and tumor and radioactive sphere activity estimates resulting from SPECT acquisitions reconstructed with different reconstruction techniques, are presented in Table 6.7. The errors displayed in this table were derived from the errors in the estimated tumor Chapter 6: Results and Discussion 86 activity values and the 2% error associated with the measurement of the true activity in a dose calibrator. These results show that in relation to the accuracy of estimated tumor activity (indicated by the relative difference parameter), the inclusion of DRC in the reconstruction algorithm has no significant affect when compared to the OSEM or FBP algorithms without corrections (p>0.05, using a paired-sample t-test). The addition of AC to the reconstruction process shows significant improvement in accuracy, and is further enhanced when DRC is also applied. Including SC in the reconstruction algorithm again significantly improves the accuracy of estimated tumor activity. It should be noted that activity is underestimated in every case, with the exception of one OSEM+AC+DRC estimate (sphere 3) and two OSEM+AC+DRC+SC estimates (spheres 2 and 3). The results detailed in this section, excluding the reconstructions that involved photon scatter correction, were presented as a poster at the European Association of Nuclear Medicine Annual Meeting 2002 [208]. Table 6.7: Relative difference between the true tumor and radioactive sphere activities and those estimated from SPECT acquisitions of the Thorax and Jaszczak phantoms. Region Volume (ml) Relative difference between the estimated activity and the truth (%) FBP OSEM OSEM+ DRC OSEM+ AC OSEM+ AC+DRC OSEM+AC +DRC+SC Thorax tumor Anterior spine 12 -93.3 ±2.4 -88.9 ±2.7 -88.6 ±2.7 -57.9 ±4.5 -23.2 ±6.6 -9.4 ±7.4 Lung base 8 -95.2 ±2.3 -94.8 ±2.3 -92.9 ±2.4 -61.4 ±4.3 -24.7 ±6.5 -4.6 ±7.7 Jaszczak sphere 6 29 -85.1 ±3.6 -75.5 ±4.7 -75.9 ±4.7 -36.8 ±9.0 -16.5 ±11.2 -3.55 ±12.6 5 16 -83.6 ±3.8 -74.2 ±4.8 -75.5 ±4.7 -47.0 ±7.8 -21.6 ±10.6 -6.6 ±12.3 4 6 -82.3 ±4.0 -69.1 ±5.4 -68.9 ±5.4 -45.7 ±8.0 -22.4 ±10.5 -4.4 ±12.5 3 3 -70.8 ±5.2 -49.5 ±7.6 -47.9 ±7.7 -24.5 ±10.3 14.2 ±14.6 35.7 ±16.9 2 2 -77.3 ±4.5 -59.9 ±6.4 -55.9 ±6.9 -57.3 ±6.7 -20.8 ±10.7 19.2 ±15.1 1 1 -93.4 ±2.7 -90.8 ±3.0 -91.8 ±2.9 * * -51.5 ±7.3 * It was not possible to differentiate the smaller radioactive spheres from the background activity. Chapter 6: Results and Discussion 87 6.1.4 Discussion For the simple calculation of activity biodistribution, performed on planar acquisitions of the 2-D simulation, the difference between the truth and the estimates of tumor activity varies from 14% to 81%. The geometric and arithmetic mean calculations produce similar results for all tumors situated on the horizontal axis of the matrix. However, the geometric method produces more accurate measurements than the arithmetic method for all other tumor positions. A target to background ratio of 6:1, which gives a more realistic estimate of the clinical situation than the 1:0 ratio, considerably increases the errors involved. Tumor C produces the activity estimate furthest from the truth in all situations. This is due to the maximum body thickness, used during calculations, being completely unsuitable for a tumor at the side of the body where the thickness is significantly smaller. Although these results are not transferable to the clinical environment due to the simple nature of this experiment, they give an indication that the use of planar acquisitions and simple biodistribution calculations are not sufficient to provide the accurate information required for tumor dosimetry calculations. The results derived from both the simple and more complex calculations of planar projections from the comprehensive simulations, agree well with our previous finding from the simple 2-D model. Planar dosimetry works best when the surrounding tissue has uniform attenuation and contains a uniform activity distribution, and when the tumor is situated in the central section of the body (e.g. the abdominal tumour). The complex method of tumour activity estimation provides a value only 5.4% from the truth in this situation. However, for a tumor at the edge of the body, adjacent to a region with non-uniform attenuation properties (e.g. the lung surface tumour), the error in the activity estimated from each method of calculation is considerable. This study shows that the complex method of tumour activity estimation provides results significantly closer to the truth than the simple method. However, it also shows the limitations of the complex method; only one value is used for the linear attenuation coefficient of the surrounding tissue, and only one body thickness measurement can be introduced. The results of the complex calculations of planar projections from the phantom experiments again reiterate the failure of planar acquisitions to allow the accurate measurement of tumor activity in regions of non-uniform attenuation. An additional factor that limits the use of planar acquisitions to estimate the biodistribution of activity is also illustrated here. Two or more regions of activity (in this case, radioactive spheres), that overlap one another in the direction of the acquisition, cannot be differentiated from each other in the resultant images. An ROI drawn around one tumor may therefore include activity from an overlapping organ, considerably reducing the accuracy of the activity estimate. The comprehensive simulation shows SPECT dosimetry (performed on OSEM+AC+DRC reconstructions) to accurately predict the activity of the tumor in the more challenging region (the surface of the lung), as a patient specific attenuation map is utilised. However, the activity in the abdominal tumor is underestimated by more than 13%. This is due to the positioning of the tumor within the camera's field of view. The abdominal tumor was located near to the edge of the camera's field of Chapter 6: Results and Discussion 88 view and therefore a significant number of photons originating within that tumor were not recorded by the camera. A complete comparison of different reconstruction techniques was performed on the data sets acquired of the phantom. Results show that the inclusion of AC or SC in the reconstruction process significantly increases the accuracy of tumor activity estimations, however the inclusion of DRC alone does not. This is because both AC and SC amend the activity (the number of counts) seen to originate in a tumor. DRC improves the resolution of the tumor but if the correct number of counts are not present (i.e. if AC and/or SC has not also been applied), then it will have no effect on the accuracy of the activity estimate. Results of these phantom experiments also show that the use of OSEM+AC+DRC+SC provides the most accurate tumor activity estimates (approximately 5% different from the truth for tumors of greater than 5ml volume). However, using this reconstruction technique the anterior spine tumor in the Thorax phantom, shows a relative difference of -9.4% to the truth. This significant underestimation of tumor activity is due not to the reconstruction technique, but to the positioning of the tumor relative to the rotation of the camera. The tumor was positioned close to the posterior edge of the phantom, and the camera heads acquired projections through 180°, from the right anterior lateral projection to the left posterior lateral projection. Therefore, for most of these projections, photons originating in the tumor experienced significant attenuation as they had to travel through the majority of the phantom to reach the camera. It is expected that projections acquired over the full 360° would provide a more accurate estimation of the activity in this tumor. In summary, the simplest method of biodistribution calculation, based on the calculation of the mean of the anterior and posterior planar images, is shown to cause large errors, particularly in the presence of background activity and tumors located at the edge of the body. The more complex method of biodistribution calculation from planar data sets, designed to correct for background activity, self-attenuation of the tumor and attenuation through the slice, is seen to work well for tumors in the central section of the body when the surrounding tissue has uniform activity and attenuation properties (giving an error of approximately 5%). However, for a tumor at the edge of the body, adjacent to a region with non-uniform attenuation properties, the error in the activity estimate is considerable (error exceeding 40%). SPECT data sets reconstructed with corrections provide noticeably more accurate biodistribution estimates than any method based on planar acquisitions, particularly for tumors in more challenging locations. The inclusion of AC in the reconstruction algorithm significantly improves accuracy, whereas the inclusion of DRC (without any additional corrections) does not. The OSEM+AC+DRC+SC algorithm provides the most accurate estimates of tumor activity (accurate to within 5% for tumors greater than 5ml in volume). Chapter 6: Results and Discussion 89 6.2 Myocard ia l Wal l Th ickness 6.2.1 Results Myocardial wall thickness, as assessed from 'healthy' phantom and normal clinical myocardial perfusion studies, was used to investigate the absolute quantitation of SPECT reconstruction techniques. MRI and 2-D echocardiography studies have shown myocardial wall thickness in adult humans to average 8-12 mm [125] [126], with maximum thickness occurring at the end-systolic point of the cardiac cycle [127]. The myocardial wall thickness of the Thorax phantom was 10 mm throughout. Table 6.8 presents the effect of reconstruction technique on the average myocardial wall thickness (Mki) of phantom and clinical data sets, for the thresholds of 45% and 50%. Table 6.8: The effect of reconstruction technique on the average myocardial wall thickness (Mki) of phantom and clinical data sets, for thresholds of 45% and 50%. Results presented + their standard deviation. Reconstruction technique Average myocardial wall thickness (mm) Phantom data sets Clinical data sets 45% threshold 50% threshold 45% threshold 50% threshold OSEM+AC+DRC+SC 21.7 + 3.2 19.2 ± 3.1 17.3 ±2 .9 15.3 ±2.9 OSEM+AC+DRC 30.8 + 4.9 26.1 ±4.0 20.0 ±3.2 18.1 ±3.2 OSEM+AC 37.6 ±3.7 33.0 ±4.3 25.2 ±5.1 22.6 ±4.5 OSEM+DRC 26.0 ±3.7 22.1 ±4.2 19.1 ±2.4 16.6 ±3.3 OSEM * 30.5 ±5.2 22.3 + 3.8 19.8 ±3.6 FBP * 32.5 ±5.7 23.4 ±4.2 20.5 ±4.2 * For data sets reconstructed with these techniques at this threshold, it was not possible to differentiate the myocardium from the surrounding background activity. For both physical phantom and clinical data sets, the application of DRC during the reconstruction provides myocardial wall thickness values significantly different from those reconstructed without DRC (paired-sample t-test: p=0.05, statistical power for clinical data sets: 80%). The utilization of AC in the reconstruction provides wall thickness values significantly different from those reconstructed without AC. A significant difference in myocardial wall thickness values is found between data sets reconstructed with OSEM and OSEM+AC+DRC, and between FBP and OSEM+AC+DRC, for clinically relevant boundary conditions, but not between FBP and OSEM. A significant difference is also found between data sets reconstructed with OSEM+AC+DRC+SC and OSEM+AC+DRC. A graphical representation of these results for phantom and clinical data sets is seen in Figure 6.1 and 6.2, respectively. The variation about the mean is depicted using Confidence Intervals of 95%. Chapter 6: Results and Discussion 90 45% 50% Threshold defining the myocardium • OSEM+AC+DRC+SC PJ OSEM+AC+DRC • OSEM+AC • OSEM+DRC r jOSEM rjFBP Figure 6.1: Myocardial wall thickness of phantom data sets comparing the quantitation of reconstruction techniques for the thresholds of 45% and 50%. 45% 50% Threshold defining the myocardium IOSEM+SC+AC+DRC • OSEM+AC+DRC I OSEM+DRC I I OSEM • OSEM+AC D F B P Figure 6.2: Myocardial wall thickness of clinical data sets comparing the quantitation of reconstruction techniques for the thresholds of 45% and 50%. Additionally, the data sets collected for this study provided invaluable knowledge on the effect of variations routinely found in myocardial perfusion scans. It is recognised that when data sets are reconstructed with FBP, myocardial quantitation software programs require separate normal heart databases or thresholds for each patient gender, radiopharmaceutical, imaging protocol, type of stress test, camera system, reconstruction technique, etc. The simulation, phantom and clinical data sets were used to determine if this assumption holds true for SPECT data sets reconstructed using OSEM+AC+DRC. All the following reconstructions were therefore carried out using OSEM+AC+DRC. No additional information was gained from the wall thickness measurements that used thresholds above Chapter 6: Results and Discussion 91 60% to define the myocardium. The following results are therefore presented for thresholds of 40% to 60% only. To investigate patient parameters, Table 6.9 presents the average myocardial wall thickness of clinical data sets from male and female patients. Table 6.9: The average myocardial wall thickness of clinical data sets from male and female patients. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) Male patients Female patients 40 20.1 ±3.5 20.2 ±2 .9 45 18.1 ±3.3 18.3±2.9 50 16.1 ±3.0 16.2 + 2.9 55 14.5 ±3.1 14.1 ±3 .3 60 12.7 ±3.4 12.1 ±3.5 Wall thickness measurements from male and female clinical groups show no significant difference (independent-sample t-test: p=0.05, statistical power: 80%). Figure 6.3 shows a graphical representation of these results. 40% 45% 50% 55% 60% Threshold defining the myocardium • Male oFemale Figure 6.3: Myocardial wall thickness of clinical data sets reconstructed using OSEM+AC+DRC, comparing male and female patients. Chapter 6: Results and Discussion 92 Table 6.10 shows the difference in average myocardial wall thickness of clinical data sets with and without the presence of close lying liver with significant tracer uptake. Table 6.10: The average myocardial wall thickness of clinical data sets with and without the presence of liver interference. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) With liver interference Without liver interference 40 20.4 ±3.3 19.7 ±3 .0 45 18.4 ±3.2 17.8 ±2 .9 50 16.1 ±3.1 16.0 + 2.8 55 14.1 ±3.2 14.3 + 3.2 60 12.2 ±3.4 12.4 + 3.5 No significant difference is found between clinical data sets with and without the presence of liver interference. Figure 6.4 shows a graphical representation of these results. _ 25 i E E 40% 45% 50% 55% 60% T h r e s o l d d e f i n i n g m y o c a r d i u m • Liver interference HNo liver interference Figure 6.4: Myocardial wall thickness of clinical data sets reconstructed using OSEM+AC+DRC, comparing data sets with and without the presence of liver interference. Chapter 6: Results and Discussion 93 Table 6.11 presents the difference in average myocardial wall thickness measured from stress and rest studies for phantom and clinical data sets. Table 6.11: The average myocardial wall thickness of stress and rest studies. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) Phantom data sets Clinical data sets Stress study Rest study Stress study Rest study 40 29.9 ±6.6 28.5 ±6.0 20.2 ±3.2 20.4 ±3.3 45 26.8 ±5.6 25.2 ±5.1 18.3 ±3 .3 18.4 ±3.0 50 23.5 ±4.3 21.8 ±4.2 16.4 ±3 .0 16.2 ±3.0 55 20.5 ±3.6 19.2 ±4.0 14.7 ±3.2 14.1 ±3.2 60 18.1 ±4.0 16.5 ±3.9 12.9 ±3.6 12.2 ±3.3 For both physical phantom and clinical data sets, acquisitions showing rest study and stress study statistics show no significant difference in myocardial wall thickness. Figure 6.5 shows a graphical representation ofthe results from clinical data sets. E 25 -, 40% 45% 50% 55% 60% Threshold defining the myocardium • Stress DRest Figure 6.5: Myocardial wall thickness of clinical data sets reconstructed using OSEM+AC+DRC, comparing rest and stress studies. Chapter 6: Results and Discussion 94 Table 6.12 presents the average myocardial wall thickness of clinical stress data sets, comparing the use of treadmill and pharmacological methods for stressing the patient. Table 6.12: The average myocardial wall thickness of clinical stress data sets, comparing the use of treadmill and pharmacological stressing techniques. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) Treadmill stress Pharmacological stress 40 19.7 ±2.9 21 .0±3 .7 45 17.5 ±2.8 19.5 ±3 .8 50 15.8±2.9 17.4 ±3 .0 55 14.3 ±3.0 15.3 ±3 .7 60 12.6 ±3.3 13.0 ±4.1 No difference is indicated between treadmill and pharmacologically stressed patients, however the statistical power of this study is not great enough to confirm this result. Figure 6.6 shows a graphical representation of these results. 40% 45% 50% 55% 60% Threshold defining myocardium • Treadmill stress rj Pharmacological stress Figure 6.6: Myocardial wall thickness of clinical data sets reconstructed using OSEM+AC+DRC, comparing treadmill and pharmacological patient stressing techniques. Chapter 6: Results and Discussion 95 To investigate the effect of phantom design, Table 6.13 presents the difference in average myocardial wall thickness resulting from different myocardium to background activity ratios in phantoms. Table 6.13: The average myocardial wall thickness of phantom data sets, comparing different myocardium to background activity ratios (3:1, 4:1, 7:1). Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) 3:1 ratio 4:1 ratio 7:1 ratio 40 35.2 + 5.5 32.8 ±5 .0 25.1 ±4.3 45 31.4 ±5.3 28.5 ±4.5 22.0 ±3.5 50 27.4 ±6.3 24.5 ±3 .7 19.2 ±2.8 55 23.0 ±6.2 2'1.2±4.0 17.3 ±3.0 60 19.3 ±5.9 18.2 ±3 .9 14.9 ±3.0 Wall thickness measurements from the physical phantoms with a myocardium to background activity concentration ratio of 4:1, are greater than those from the 7:1 phantoms, but not significantly different from those from the 3:1 phantoms. Figure 6.7 shows a graphical representation of these results. Figure 6.7: Myocardial wall thickness of phantom data sets reconstructed using OSEM+AC+DRC, comparing myocardium to background ratios of 7:1, 4:1 and 3:1. Chapter 6: Results and Discussion 96 Table 6.14 presents the difference in average myocardial wall thickness measured from a beating and static model heart in simulated data sets. Table 6.14: The average myocardial wall thickness of simulated data sets, comparing beating and static heart models. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) Beating heart Static heart 35 23.2 + 2.9 19.3 ±2 .9 40 19.7 ±2.0 16.9 ±2 .0 45 17.4 ± 1.9 14.6 ±2 .3 50 15.1 ±2.3 13.0 ±1 .9 55 1 2 8 ± 2 . 8 10.7 ±2 .5 Measurements of wall thickness from the beating heart are significantly larger than those from the static heart for the computer simulated acquisitions of the MCAT phantom. Figure 6.8 shows a graphical representation of these results. 35% 40% 45% 50% 55% Threshold defining the myocardium • Beating heart • Static heart Figure 6.8: Myocardial wall thickness of simulation data sets reconstructed using OSEM+AC+DRC, comparing a static and beating model heart. Chapter 6: Results and Discussion 97 To investigate the effect of acquisition parameters, Table 6.15 presents the average myocardial wall thickness of the phantom acquired with and without an image zoom. These data sets were reconstructed using OSEM+DRC as no transmission scan could be acquired. Table 6.15: The average myocardial wall thickness of phantom data sets, comparing acquisitions with and without a zoom. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) With zoom Without zoom 40 20.3 + 3.2 23.9 ±4.5 45 17.3 ±3.5 20.5 ±4 .0 50 14.8 ±3.4 17.7 ±3.5 55 12.8 ±3.8 14.7 ±4 .7 60 10.0±4.1 12.5 ±5.4 Zoomed and non-zoomed acquisitions (reconstructed with no AC), show significantly different measurements of wall thickness for physical phantom experiments. Zoomed images produce results closer to the truth for appropriate thresholds. To investigate the effect of post reconstruction processing, Table 6.16 presents the effect of spatial filters on the average myocardial wall thickness of the phantom. These data sets were again reconstructed using OSEM+AC+DRC. Table 6.17 presents the effect of spatial filters on the average myocardial wall thickness of clinical data sets. Table 6.16: The effect of spatial filters on the average myocardial wall thickness of the phantom. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) Gaussian (kernel size [3 3 3], standard deviation 0.75) Butterworth (cut-off 0.5, order 5) Butterworth (cut-off 0.3, order 10) 40 * 36.0 ±4 .9 41.9±4.3 45 36.0 ±4.7 30.8 ±4.7 38.0 ±4.8 50 31.2 ±4.2 26.1 ±4.0 34.8 ±4.1 55 26.7 ± 3.7 22.5 ±2.9 31.1 ±4.8 60 23.3 ±2.9 20.1 ±3.8 27.6 ±4.4 * It was not possible to differentiate the myocardium from the surrounding background activity in this situation. Chapter 6: Results and Discussion 9 8 Table 6.17: The effect of spatial filters on the average myocardial wall thickness of clinical data sets. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) Butterworth (cut-off 0.5, order 5) Butterworth (cut-off 0.3, order 10) 40 21.9 ±3.4 29.6 ±4.4 45 20.0 ±3.2 26.6 ±3 .9 50 18.1 ±3.2 24.1 ±3 .7 55 16.0 ±3.1 21.9 ±3 .8 60 13.9 ±3.3 19.4 ±4 .2 Each spatial filter provides wall thickness measurements significantly different from the other filters for phantom experiments and clinical data sets. The sharp Butterworth filter with cut-off 0.55 and order 5 provides the smallest wall thickness and the smooth Butterworth with cut-off 0.3 and order 10 provides the largest. The Gaussian filter with a standard deviation of 0.75 falls between the two Butterworth filters. Figure 6.9 shows a graphical representation of these results for phantom experiments. i 5 0 l 40% 45% 50% 55% 60% Threshold defining myocardium • Gaussian (kernal size [3 3 3], standard deviation 0.75) • Butterworth (cutoff 0.5, order 5) II Butterworth (cutoff 0.3, order 10) Figure 6.9: Myocardial wall thickness of phantom data sets, reconstructed using OSEM+AC+DRC, comparing the effect of spatial filters. Chapter 6: Results and Discussion 99 Table 6.18 presents the effect on the average myocardial wall thickness of the phantom, of interpolating data sets from 128 x 128 x 128 matrices onto 256 x 256 x 256 matrices. Table 6.18: Effect on the average myocardial wall thickness of the phantom, of interpolating data sets from 128 x 128 x 128 matrices onto 256 x 256 x 256 matrices. Results presented ± standard deviation. Threshold defining the myocardium (%) Average myocardial wall thickness (mm) 128 x 128 x 128 matrix 256 x 256 x 256 matrix 40 36.0 ±4.9 33.2 ±4 .3 45 30.8 ±4.7 28.0 ±3 .8 50 26.1 ±4.0 24.1 ±2 .8 55 22.5 ±2.9 20.7 ±2 .9 60 20.1 ±3.8 17.7 ±2 .8 The wall thickness measurements from data sets interpolated from 128 x 128 x 128 matrices onto 256 x 256 x 256 matrices are significantly closer to the truth than those from the original 128 x 128 x 128 data sets for the phantom experiments. Figure 6.10 shows a graphical representation of these results. Jinn 50% 55% 60% defining the myocardium • 128x128 matrix E3256x256 matrix i Figure 6.10: Myocardial wall thickness of phantom data sets reconstructed using OSEM+AC+DRC, comparing original and interpolated matrix sizes for all thresholds. 1 t u T 2 35 IB | 30 0 25 | 20 | 15 .2 10 « 5 o 1 0 S 40% 45% Thresho The results from this section were presented in poster form at the IEEE Medical Imaging Conference 2004 [209]. Chapter 6: Results and Discussion ,100 6.2.2 Discussion The myocardial wall thickness of 'healthy' phantoms and normal patient data sets were used to compare the absolute quantitation of different SPECT reconstruction techniques. As was expected, different reconstruction techniques change the absolute quantitation of myocardial perfusion scans. The addition of DRC to any reconstruction reduces the wall thickness to a value closer to the truth. The true thickness of the myocardial wall is of comparable size to the resolution of a SPECT reconstruction. Any improvement in image resolution, such as that caused by the inclusion of DRC in the reconstruction technique, will therefore result in a more accurate myocardial wall thickness. The inclusion of AC in the reconstruction process increases myocardial wall thickness to a value further from the truth. This is due both to the proportional increase in counts seen at this depth in the patient, and the enhanced influence of photon scatter. When AC and DRC are applied simultaneously an overall improvement in accuracy is seen. These results indicate that in the pursuit of quantitative myocardial perfusion studies, AC should not be applied without the additional application of DRC. The OSEM+AC+DRC+SC reconstruction provides myocardial wall thickness measurements closer to the truth than any other technique. It should be noted however, that the application of SC significantly increases the time required for the reconstruction of a data set (approximately 5 hours computational time required for OSEM+AC+DRC+SC compared to approximately 30-40 minutes for OSEM+AC+DRC, using a Pentium 4, 1.5 GHz processor). A reconstruction that takes a significant amount of time could prove prohibitive in a routine clinical environment. The conclusions derived of these results are reinforced as, in every case, the results obtained from clinical data sets concur with the results obtained from phantom data sets. However, as can be observed from Table 6.8, the myocardial wall thickness measurements obtained from the Thorax phantom (true value 10 mm, static heart) are significantly larger than those obtained from the clinical data sets (approximate true value 8-12 mm, beating heart). This is due to a discrepancy in the set-up of the Thorax phantom; as the activity administered to the LV cavity was smaller than the sensitivity of the ionisation chamber, its measurement was inexact and more activity was added to the region than was intended. Although this resulted in extended myocardial wall thickness measurements, the activity in the LV cavity was consistent throughout each 'healthy' phantom acquisition. As a result comparisons made between different phantom acquisitions hold true. For subsequent acquisitions of the Thorax phantom containing myocardial infarcts, a method involving dilution was used to measure the LV cavity activity in order to remove this problem. Additionally, the data sets collected for the analysis above were used to determine if numerous normal heart databases would be required to perform myocardial quantitative analysis on OSEM+AC+DRC reconstructed data sets. The myocardial wall thickness of clinical and phantom data sets were compared for numerous patient, acquisition and post-reconstruction processing. Table 6.19 Chapter 6: Results and Discussion 101 shows a summary of the results together with an indication as to whether separate databases would be required to accurately analyse data sets from, for example, both male and female patients. Table 6.19: Summary of wall thickness measurement comparisons of patient, acquisition and post-reconstruction processing parameters. From these results the requirement for a separate normal heart database for myocardial quantitation is predicted. Significant difference seen in phantom data* (p=0.05) Significant difference seen in clinical data (p=0.05, Power=80%) Separate normal heart database required when data sets are reconstructed using OSEM+AC+DRC Comparison of patient variables Male and females - no no With and without liver interference no no Rest and stress studies no no no Treadmill and pharmacological stress no no Comparison of acquisition and post-reconstruction processing variables With and without acquisition zoom yes yes Different reconstruction techniques yes yes yes Different spatial filters yes yes yes 128x128x128 and 256x256x256 matrices yes yes *ln this table 'phantom data' describes the acquisitions of both physical and simulation phantoms. This comparison of myocardial wall thickness does not provide a definitive answer to whether separate databases would be required to quantitatively analyse myocardial perfusion data sets reconstructed using OSEM+AC+DRC. It does however provide a indication that the variations seen in patients would no longer require separate databases, and this would significantly reduce the workload of clinical centres setting up new quantitation software. It is determined that myocardial wall thickness measurements from normal patients are not dependent on the presence or absence of liver interference when reconstructed using OSEM+AC+DRC. However, as the visualisation of the heart and any infarcts present will still be Chapter 6: Results and Discussion 102 enhanced by the removal of such an organ from the image, the Liver Removal section of iQuant continues to play a useful role. It has been shown that the application of an acquisition zoom, or the interpolation of the reconstructed data set onto a 256x256x256 matrix, significantly reduces the measured myocardial wall thickness. This outcome is due to a decrease in the volume of each voxel (111 mm3 reduced to 33 mm3 for a zoomed acquisition, or 14 mm3 for a 256x256x256 matrix), equivalent to an increased sampling frequency and a subsequently more accurate measurement of the edge of the myocardial wall (a reduction of the partial volume effect). However, this improvement comes at the price of a decreased signal-to-noise ratio. Although the studies carried out on phantom and clinical data sets to determine myocardial wall thickness allowed the comparison of a number of variables commonly seen in the clinical environment, it is not an exhaustive list as it was not possible to study all variables. Additional factors that may affect myocardial wall thickness even when data is reconstructed with OSEM+AC+DRC are radioisotope (201TI or 9 9 mTc), collimator type (LEHR or LEUHR), patient stance (prone or supine), and patient body habitus (ethnic origin). The measurement of myocardial wall thickness was also used to compare the characteristics of both simulation and physical phantoms. The OSEM+AC+DRC reconstruction of a static heart simulation shows a myocardial wall thickness significantly smaller than that of a beating heart simulation. This is because the beating heart data set is showing an average of the myocardium moving through time. A suitable analogy would be a 1 s photographic exposure of a galloping horse, which would show a blurred image of the animal extending to a length much longer than its true size. Myocardial perfusion studies can be acquired with a gating of the cardiac cycle. In effect 16 images are acquired of the heart in a different phase of the cardiac cycle, allowing the production of a moving image of the beating heart. However, as the total number of counts are split into 16 time frames, the statistical noise associated with each frame is significant. Any extraction of quantitative data would be significantly affected by this noise. Physical phantoms which contain a low concentration of background activity compared to myocardial activity (the 7:1 ratio phantom), provide myocardial wall thickness measurements closer to the truth for realistic thresholds, than phantoms with a higher background activity. This is because the reconstruction of the myocardium in a low background activity is easier and therefore more accurate even for FBP. However, as was observed from the study of clinical data sets, a 7:1 ratio of myocardial to background activity concentrations is not commonly seen in routine clinical studies, a more realistic value is 4:1. As quantitation is effected by the myocardium to background activity ratio, phantoms used to simulate clinical studies should always contain clinically relevant activity ratios both in the myocardium and background, and also in perfusion defects and within the LV cavity. In summary the quantitative value of myocardial wall thickness allows the comparison of absolute quantitation in data sets reconstructed using different techniques. The inclusion of DRC in the Chapter 6: Results and Discussion 1 0 3 reconstruction process reduces the myocardial wall thickness to a value closer to the truth, whereas the inclusion of AC increases the wall thickness. AC should therefore never be applied without the inclusion of DRC. The reconstruction process OSEM+AC+DRC+SC provides myocardial wall thickness measurements closer to the truth than any other technique. These data sets also allowed a number of variations commonly seen in clinical myocardial perfusion studies to be compared. Patient gender, the presence or absence of liver interference, rest or stress studies, the type of stress test, and clinically relevant variations in myocardium to background activity concentrations, are found to have no significant effect on myocardial wall thickness when reconstructions include with AC and DRC. This indicates that the use of OSEM+AC+DRC as the routine clinical reconstruction algorithm would reduce to one, the number of normal heart databases or thresholds required for quantitative myocardial analysis. The use of smaller voxels results in greater accuracy, as does a low concentration of background activity compared to myocardial activity. The strength of this comparative study lies in the similar trends observed in both phantom data sets and clinical data sets. Chapter 6: Results and Discussion 104 6.3 Sof tware Va l idat ion The image quantitation software iQuant was developed for this thesis. Before iQuant could be used to measure myocardial infarct size, it was necessary to determine the boundary condition thresholds that would define viable myocardium for different reconstruction techniques. It was also necessary to validate the accuracy and reliability of its methodology and to compare its results to those derived from other, well established, myocardial quantitation software programs. 6.3.1 Boundary condition thresholds 6.3.1.1 Thresholds suggested from myocardial wall thickness studies The threshold that would be used to define viable myocardium was suggested by the results collected for the myocardial wall thickness investigations with 'healthy' phantoms (containing no infarcts) and normal patient data sets. During these investigations observations were made as to the lowest threshold at which the VOI of the viable myocardium contained unexpected defects or holes. Particularly in the case of the physical phantom, where the thickness of the each wall was known to be identical, no defects should occur. In clinical data sets it is known that the apex of the LV is thinner than the other walls [192], therefore defects are more likely to occur in this region. At the thresholds of 35%, 40%, 45% and 50%, and for every reconstruction technique, no defects were seen in the phantom data sets. Table 6.20 presents the number of clinical data sets that contained defects at these thresholds. Table 6.20: The number of holes that appear in the viable myocardium VOI of normal clinical data sets. Reconstruction technique Number of data set containing holes at these applied thresholds (total number of data sets observed) 35% threshold 40% threshold 45% threshold 50% threshold OSEM+AC+DRC+SC 2 (20) 4(20) 10(20) 14 (20) OSEM+AC+DRC 0(74) 2(74) 11 (74) 27 (74) OSEM+AC 0(20) 0(20) 1 (20) 4 (20) OSEM+DRC 0 (20) 2(20) 3(20) 7(20) OSEM 0(47) 0(47) 4(47) 14 (47) FBP 0 (20) 0(20) 0(20) 1 (20) 6.3.1.2 Thresholds determined from myocardial infarct size studies The phantom experiments and computer simulations, acquired with a variety of infarct sizes, locations and severities, were used to determine the exact viable myocardium threshold of iQuant. The threshold that produced the measurement of myocardial infarct size closest to the truth was determined for each phantom and simulation reconstructed with every technique. The thresholds for the phantoms displaying different sizes and locations of infarct are presented in Table 6.21, and thresholds for Chapter 6: Results and Discussion 105 different severities of infarct are presented in Table 6.22. Table 6.23 displays thresholds for infarcts with and without the presence of liver interference, and Table 6.24 displays thresholds for sets of data interpolated onto a larger matrix. Data sets from the phantom containing the very small infarct were not used in this analysis as these infarcts were not visible in several reconstructions and therefore comparisons could not be drawn between reconstructions. Table 6.21: Thresholds that produce the myocardial infarct size measurements closest to the truth for different sizes and location of infarct in the phantom. Infarct size Infarct location Threshold (% of maximum myocardial counts) OSEM+ AC+DRC+SC OSEM+ AC+DRC OSEM+ AC OSEM+ DRC OSEM FBP Large Ant 35 45 50 45 50 50 Inf 35 40 45 40 40 45 Lat 35 45 50/55 55 50 50 Sep 35/40 50 50 40 45 45 Medium Ant 35 50 55 45 50/55 50 Inf 35 45 45/50 40 45 45 Lat 40 50 55 45 50 50 Sep 35 45/50 55 40 50 50 Small Ant 35 45 50 45 55 55 Inf 40 50 50 40/45 45/50 45 Lat 30 45 50 35/40 45 45/50 Sep 35 45 55 40/45 50 50 Table 6.22: Thresholds that produce the myocardial infarct size measurements closest to the truth for different activity concentrations of the small, inferior wall infarct in the phantom. Infarct activity concentration (kBq/ml) Threshold (% of maximum myocardial counts) OSEM+AC +DRC OSEM+ AC OSEM+ DRC OSEM FBP 50 40 45/50 35 40 40 100 50 50 40/45 45/50 45 200 50 50 35 45/50 40/45 Chapter 6: Results and Discussion 106 Table 6.23: Thresholds that produce the myocardial infarct size measurements closest to the truth for the small, inferior wall infarct in the phantom containing a close lying liver. Close lying Threshold (% of maximum myocardial counts) liver OSEM+AC+DRC OSEM+ AC OSEM+ DRC OSEM FBP Present 50 55 35 45 40 Absent 50 50 40/45 45/50 45 Table 6.24: Thresholds that produce the myocardial infarct size measurements closest to the truth for the inferior wall infarcts of the phantom interpolated onto a larger matrix. All reconstructed with OSEM+AC+DRC. Infarct size Threshold (% of maximum myocardial counts) 128x128x128 matrix 256x256x256 matrix Large 40 40 Medium 45 40 Small 50 45 Very small 55/60 50/55 The thresholds for the computer simulations of the static heart produced similar thresholds to the phantom experiments. Table 6.25 displays the thresholds for different locations of the medium infarct for both the static and beating heart simulations. Table 6.25: Thresholds that produce the myocardial infarct size measurements closest to the truth for different locations of the medium infarct in the static and beating heart simulations. Heart model Infarct location Threshold (% of maximum myocardial counts) OSEM+AC +DRC OSEM+ AC OSEM+ DRC OSEM FBP Static Ant 50 50 45 45 50 Inf 60 50 40/45 55 45 Lat 50 45 50 50/55 50 Sep 55/60 50/55 40 45 50 Beating Ant 55 50 40 40/45 45 Inf 60 60 45 50 45 Lat 55 55 50/55 50/55 55 Sep 60 60 45 45/50 60 Chapter 6: Results and Discussion 107 For each reconstruction technique and every infarct size, there are no discernible trends in the thresholds derived from infarcts of different location. For each reconstruction technique and every infarct location, there is no change in the thresholds when different infarct sizes are considered. However, the use of different reconstruction techniques does have a noticeable effect on thresholds. A lower threshold is required for reconstructions including DRC and an even lower threshold for reconstructions including SC. The infarcts containing a lower concentration of activity require, in general, a lower threshold to be detected accurately by iQuant. The presence of liver interference does not effect the threshold for the more complex reconstruction techniques. For three out of the four infarct sizes investigated, a lower threshold is required by the interpolated 256x256x256 matrix. The thresholds for the beating heart simulation are 5% higher than those for the static heart in approximately half of the simulations. These results were used to determine the thresholds that iQuant employs to define viable myocardial tissue for the measurement of myocardial infarct size. It is clear that separate thresholds are required for different reconstruction techniques, and may be required for different voxel sizes (matrix size different from 128x128x128). It is possible to implement the use of separate thresholds in these situations as they are known before iQuant is initiated. The choice of threshold cannot depend upon the location, size or severity of the defect as these parameters are not known before an infarct size is measured. Our results confirm that different thresholds are not required for these situations, particularly for infarct severities commonly seen in clinical studies. Therefore, thresholds were chosen for their ability to determine myocardial infarct size of phantom data sets accurately over a range of infarct sizes and locations. Table 6.26: The thresholds used for measurement of myocardial infarct size in iQuant. Reconstruction technique Most suitable threshold to accurately measure myocardial infarct size (% of maximum myocardial counts) OSEM+AC+DRC+SC 35 OSEM+ AC+DRC 45 OSEM+ AC 50 OSEM+ DRC 45 OSEM 50 FBP 50 Where two adjacent thresholds provided infarct size measurements equally close to the truth, the upper threshold was chosen. This was done as the computer simulation data sets indicated that a higher threshold may be more suitable for a beating heart (a prerequisite for clinical data) as compared to the static heart (represented in the physical phantom). The final thresholds chosen to be implemented Chapter 6: Results and Discussion 108 into the iQuant software to allow accurate measurement of myocardial infarct size, are presented in Table 6.26. 6.3.2 iQuant accuracy The accuracy of the iQuant method was determined using the original, beat ing heart M C A T model, with no MC simulat ions. Results are presented in Figure 6 .11 . The true size of the measured infarct varied from 13.8% to 1 9 . 1 % throughout the cardiac cycle, with an average value over t ime of 15.4% of the total myocard ium. Anterior Inferior Lateral Location of myocardial infarct • True size El Measured size Figure 6.11: Infarct size determined with iQuant of the original M C A T model wi th a beating heart. The black columns represent the true average volume of the infarct and the bar extending f rom the columns represent the change in vo lume seen during the cardiac cycle. Each grey co lumn represents the mean ± standard deviation of a series of four measurements. The absolute difference between the true infarct size (averaged over t ime) and the value measured with iQuant was calculated for each infarct location. Averaged over all infarct locations the absolute difference is 0.27 ± 0 .29% of the total myocardium (mean ± standard deviat ion). This is equivalent to 0.44 ml in a 23.4 ml infarct (myocardial volume 152.1 ml), or 4 voxels in a 230 voxel infarct (myocardial volume 1500 voxel on a 128 x 128 x 128 matrix). Chapter 6: Results and Discussion 109 6.3.3 iQuant reliability The reliability of iQuant was determined from measurements of myocardial infarct size performed by three trained observers on five independent scans of the Thorax phantom. The measurements recorded by these observers are presented in Table 6.27. From these results the following parameters were calculated: The inter-observer reliability coefficient is 0.73. This is the correlation coefficient when two observers measure the same target, in this case, the same infarct [207]. The intra-observer variation is 0.159% of the total myocardium. This is a measure of variance (a2), and describes the variation seen when one observer repeatedly measures the same target. It was calculated within each observer across all three observers. The standard error, or the standard deviation (a) within a group for all three groups, is 0.399% of the total myocardium. Table 6.27: Reliability study, 3 independent observers measurement of myocardial infarct size from 5 identical phantoms. Infarct placed in the inferior wall and 5.3% ofthe total myocardium in size. Phantom acquisition Infarct size (% of total myocardium) Observer 1 Observer 2 Observer 3 A 5.60 4.96 6.69 B 6.06 4.92 5.96 C 5.25 5.08 6.86 D 6.50 4.99 6.82 E 5.70 5.07 5.72 6.3.4 Comparison to established myocardial quantitation programs To further validate the measurement of myocardial infarct size with iQuant, both phantom and clinical data sets were used to compare infarct size measurements taken from iQuant, with those obtained from other, well established, myocardial quantitation software programs. 6.3.4.1 Comparison with Mayo Clinic software The myocardial infarct size of the phantom containing the solid infarct inserts, was analysed by the Mayo Clinic and using iQuant. The results of this analysis is presented in Table 6.28. Chapter 6: Results and Discussion 110 Table 6.28: Myocardial infarct size of the solid insert phantom, measured by the Mayo Clinic and using iQuant. True infarct size (% of total myocardium) Measured infarct size (% of total myocardium) Mayo Clinic method iQuant method 0 0 0 6 6 5.1 10 10 8.9 21 20 18.9 29 33 33.0 40 43 46.7 50 53 52.1 61 * 55.1 71 72 68.2 * This data set could not be recovered from the disc. Linear regression analysis was performed to compare both sets of measurements with the true infarct size (Figure 6.12 and 6.13). The parameters resulting from this analysis are presented in Table 6.29. .3 8 0 1 0 20 40 60 True infarct size (% of myocardium) Figure 6.12: Linear regression analysis carried out on the Mayo Clinic measurements of myocardial infarct size, on the phantom containing solid infarct inserts, reconstructed with FBP. Chapter 6: Results and Discussion 111 0 10 20 30 40 50 60 70 80 True in farc t s i ze (% of m y o c a r d i u m ) Figure 6.13: Linear regression analysis carried out on the iQuant measurements of myocardial infarct size, on the phantom containing solid infarct inserts, reconstructed with FBP. Table 6.29: The parameters of linear regression analysis performed on the Mayo Clinic and iQuant measurements of myocardial infarct size. Parameter Mayo clinic method iQuant method Slope 1.04 0.97 Intercept 0.20% 0.82% Correlation coefficient 0.996 0.977 Mean absolute error 1.50% 2.84% 6.3.4.2 Comparison with 4D-MSPECT software The myocardial infarct size of clinical data sets acquired from patients post Ml, were analysed using both the 4D-MSPECT and iQuant methods. However, before the 4D-MSPECT analysis was performed, the software was adapted to perform analysis using a threshold rather than a normal heart database. This was done to ensure that infarct size could be determined without interference from ischemic tissue which the database is designed to detect. Using the same method as described in section 6.3.1.2 Threshold determined from myocardial infarct size studies, the threshold that produced myocardial infarct size measurements closest to the truth was determined as 55% for the FBP reconstruction technique. The myocardial infarct size of 22 patients post Ml, reconstructed using FBP, were measured using both 4D-MSPECT and iQuant. The results, together with the notes of the cardiologist reporting on the 4D-MSPECT results, and observations as to the relative length of the septal and lateral walls, are presented in Table 6.30. Technical quality of the scans were considered good in all cases. Chapter 6: Results and Discussion 11 Table 6.30: Myocardial infarct size measurement from clinical data sets reconstructed with FBP. Patient # Infarct size measurement (%) Notes from cardiologist* Septal wall significantly shorter than lateral wall** 4D-MSPECT iQuant 1 20 21.7 inf 2 19 20.2 inf S 3 28 33.6 ant X 4 32 33.4 ant X 5 10 8.0 inf 6 10 9.2 inf 7 0 0.0 normal 8 12 16.7 inf 9 10 9.1 inf 10 33 28.9 ap 11 12 11.5 inf 12 9 8.3 inf 13 0 0.0 normal X 14 2 4.2 inf •/ 15 0 0.0 normal 16 7 16.6 inf X 17 1 0.0 ant 18 10 17.3 inf X 19 8 13.5 inf 20 0 0.0 normal X 21 21 26.5 inf X 22 38 44.6 ant X * Cardiologist notes: inf = inferior wall infarct, ant = anterior wall infarct, ap = apical infarct, normal = no infarct, septal wall significantly shorter than lateral wall, x = septal wall of similar length to lateral wall. Chapter 6: Results and Discussion 113 6.4.3 Discussion Before iQuant could be used to measure myocardial infarct size, the thresholds of viable myocardium were determined for each reconstruction technique using simulations and phantom studies containing myocardial infarcts. A 50% threshold was found to define viable tissue in FBP, OSEM and OSEM+AC reconstructions, a 45% threshold defined viable tissue for OSEM+DRC and OSEM+AC+DRC, and 35% defined viable tissue for OSEM+AC+DRC+SC. The thresholds may be specific to voxel size and system resolution, therefore these factors (dependent on acquisition zoom, matrix size and collimator type) should be keep constant. Additionally the computer simulations (voxel size 3.6 mm) are not used in subsequent analysis of myocardial infarct size as the thresholds were determined from phantom data sets (voxel size 4.8 mm). The 'healthy' phantom (containing no infarcts) showed no defects when these thresholds were used to define the myocardial VOI. However, some apical defects did occur in the normal patient data sets when these thresholds were used, though in each case the defect was never larger than a few voxels in size and would therefore be considered clinically irrelevant if it were measured at all. It is known that apical defects are sometimes apparent in myocardial perfusion studies of normal hearts. The reason is twofold. Firstly the apex of the myocardium is thinner than the inferior, anterior, lateral and septal myocardial walls [192]. The second reason is due to the partial volume effect and explains why this phenomena is also occasionally seen in phantom experiments where the apex of the myocardium is of equal thickness to the other walls. The partial volume effect is graphically described in Figure 6.14. When the myocardial wall lies obliquely across the voxels (as all myocardial walls do during acquisition and reconstruction), voxels entirely within the region of the wall are assigned high counts but voxels only partially within the wall are assigned lower counts. As the diagonal dimension of each voxel is of a similar order of magnitude to the thickness of the myocardial wall, this results in the inconsistent appearance of the wall and occasionally in holes, or defects. The partial volume effect is exaggerated in the myocardial apex as it curves in two dimensions and therefore lies oblique to all three axes of the voxel matrix. To reduce the partial volume effect the data sets can be interpolated onto a larger matrix [210]. However, during the infarct size measurement of the interpolated 256 x 256 x 256 matrix, it was noted that not only did the interpolation itself take approximately 15 minutes, but the measurement of infarct size took a considerably longer time to complete. This was due to the increased number of voxels involved. Although the process was time consuming, it was no more difficult for the operator than measuring the 128 x 128 x 128 matrix data set. It should also be noted that any increase in matrix size would be associated with a significant decrease in signal-to-noise ratio. Chapter 6: Results and Discussion 114 ial Colour scale: High counts Low counts Figure 6.14: The partial volume effect on the myocardial wall. For a 15.4% myocardial infarct the measurement of myocardial infarct size with iQuant is accurate to within an average of 0.3% of the total myocardium. This value was determined by measurement of the MCAT model, not an acquisition of the object as this would insert essentially unknown variables such as the random statistics of radioactive decay, the effect of pixelization, and the accuracy of the reconstruction technique. This is an exceptionally good result and the small variation from the truth is partly due to the interpolation required by the reorientation process (an inescapable unknown variable). However when iQuant is used to measure the infarct size from SPECT data sets (that have been acquired and reconstructed), its 'accuracy' will appear to degrade. This is due to factors that are related to the process of data collection in nuclear medicine and not to the capability of iQuant. However, these factors were incorporated in the measurement of reliability. For inter-observer reliability a perfect result is 1 and a result of >0.75 is defined by [207] as excellent for a clinical test. A result of between 0.4 and 0.75 is considered good [207]. Using these definitions, the result of 0.73 achieved by iQuant shows very good inter-observer reliability. The intra-observer variation is a measure of variance, and the perfect result would be 0. The result of 0.159% of the total myocardium achieved by iQuant is also good. It should be emphasized that the intra-observer variation was measured across all three observers, regardless of their experience. Observer 2 had knowledge of the iQuant program and over 3 years experience of clinically reporting myocardial perfusion scans, whereas observers 1 and 3 had comprehensive knowledge of the iQuant method but limited clinical experience. The standard deviation within the measurements of observer 2 alone produces an intra-observer variation of just 0.005 % 2. This suggests that intra-observer variation will improve with further clinical training and experience of observers. Chapter 6: Results and Discussion 115 The Mayo Clinic and iQuant methods of myocardial infarct size measurement produced similar results when compared to the truth using linear regression analysis. The solid insert phantom used in this study represented a simplified situation as the myocardium to background activity ratio was large, and no activity was present in either the LV chamber or in the myocardial infarct inserts. This latter fact inhibited the iQuant operator in locating the exact boundaries of the infarct. However, even under these conditions, iQuant performed with comparable accuracy to the Mayo Clinic method. During the 4D-MSPECT measurement of myocardial infarct size from phantom data sets, it was noticed that even large thresholds did not accurately measure the large infarct, its size was always underestimated. From the comparison of infarct size measured from clinical data sets using 4D-MSPECT and iQuant it is clear that iQuant consistently measures infarct sizes to be larger than the 4D-MSPECT measurements. It is likely that this difference is due to iQuants ability to detect the thinning of the myocardium at the borders of the infarct. The 4D-MSPECT software requires the creation of a polar map and this software produces the polar map by sampling the counts of the mid-myocardial surface. Therefore, even if the wall is very thin, if the value in its centre is above the threshold then it will not contribute to the infarct size. It was determined through inspection of the myocardial perfusion study database of normal patients (collected for the myocardial wall thickness analysis), that a difference in length between the lateral and septal walls (equivalent to a basal shortening of the septal wall) is a normal occurrence and does not indicate myocardial infarction or ischemia. Due to the use of the polar map, 4D-MSPECT reports the basal shortening as an infarct (Figure 6.15). For the measurements of infarct size reported in this study the portion of the total infarct size attributed to the septo-basal wall was visually estimated and manually subtracted from the total infarct size (unless it was contiguous to a genuine infarct). This method is not ideal as the myocardial volume, used to calculate the size of the infarct as a percentage, is overestimated as it includes the incorrectly extended septal wall. 4D-MSPECT cannot be altered to automatically take the basal shortening of the septal wall into account. If the basal slice picked to limit the polar map production is moved towards the apex to remove any septal wall shortening, then the overall size of the LV decreases, falsely increasing the relative size of any infarct contained within it. Also any infarcts at the basal end of the other myocardial walls will also be removed from the investigation. In addition to the work presented in this thesis, the iQuant software has been used to measure infarct sizes for other recent experiments and investigations: as a measure for comparing the accuracy of emission data sets reconstructed using attenuation maps containing a range of artefacts commonly seen in the-clinical environment [196]; and as a method of analysing different scatter correction techniques [18]. Chapter 6: Results and Discussion 116 Figure 6.15: 4D-MSPECT polar map showing the genuine apical infarct and the appearance of basal shortening of the septal wall as a second infarct. In summary iQuant has been shown as an accurate and reliable method of measuring myocardial infarct size, comparing well with established myocardial quantitation software. Its advantages over commercially available techniques include its ability to determine an infarct size in 3-D (without the use of a 2-D polar map), and without the dependence on a normal heart database. Chapter 6: Results and Discussion 117 6.4 Myocardial Infarct Size 6.4.1 Phantom experiments The phantom experiments containing infarct inserts were used to determine the quantitative effect on myocardial infarct size of different SPECT reconstruction techniques. Results were organised into graphs for each location of infarct and each reconstruction technique. The graphs contain data from 5 measurements of 3 different infarct sizes. Linear regression analysis was performed on each graph to determine the relationship between the true size of the infarct and that measured from the reconstructed data sets. Figures 6.16 to 6.21 present the graphs of the inferior wall infarct for each reconstruction technique. The graphs depicting the measurement of the anterior, lateral and septal wall infarcts can be found in Appendix C. Figure 6.16: Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Chapter 6: Results and Discussion 118 25 i 7 20 -,N '3S o 15 c £ 10 -y = 1.3266X-3.5469 R2 = 0.9719 0 5 10 15 20 True infarct size (%) Figure 6.17: Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Figure 6.18: Linear regression analysis carried out on OSEM+AC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Chapter 6: Results and Discussion 119 30 i £ 10 0 I y = 1.4923x- 1.3455 R2 = 0.9519 0 5 10 15 20 True infarct size (%) Figure 6.19: Linear regression analysis carried out on OSEM+DRC reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. 40 35 30 25 20 15 10 5 0 y = 1.5593 R2 = 0 x-2.3531 .8406 t 10 True infarct size (%) 15 20 Figure 6.20: Linear regression analysis carried out on OSEM reconstruction ofthe inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Chapter 6: Results and Discussion 120 30 25 20 15 10 5 10 True infarct size (%) 15 20 Figure 6.21: Linear regression analysis carried out on FBP reconstruction of the inferior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. The slopes of the linear regression analysis carried out on each graph, together with the error of the slopes are presented in Table 6.31. The correlation coefficients of the linear regression analysis are presented in Table 6.32. Table 6.31: The slopes of the linear regression analysis carried out on 5 measurements of 3 sizes of myocardial infarct size (phantom data). The errors in the slopes were calculated as part of the linear regression analysis. A slope of greater than 1.0 shows an overestimation in infarct size and a slope of less than 1.0 shows an underestimation. Reconstruction technique Slope of linear regression analysis Inferior wall infarct Anterior wall infarct Lateral wall infarct Septal wall infarct OSEM+AC+DRC+SC 1.13 + 0.04 0.93 ±0.02 0.85 ±0.06 0.76 + 0.05 OSEM+AC+DRC 1.33 ±0.06 0.90 ± 0.07 0.82 ±0.05 0.66 ± 0.06 OSEM+AC 1.34 ±0.08 0.83 ± 0.07 0.77 ±0.05 0.77 ±0.10 OSEM+DRC 1.49 ±0.09 1.10±0.08 0.46 ± 0.05 1.38±0.14 OSEM 1.56 ± 0.19 0.77 ± 0.05 0.54 ±0.05 1.51 ±0.15 FBP 1.30±0.10 0.86 ± 0.04 0.66 ± 0.06 1.59±0.18 Chapter 6: Results and Discussion 121 Table 6.32: The correlation coefficients (R2) of the linear regression analysis carried out on 5 measurements of 3 sizes of myocardial infarct size (phantom data). Reconstruction technique Correlation coefficients {Rz) of linear regression analysis Inferior wall infarct Anterior wall infarct Lateral wall infarct Septal wall infarct OSEM+AC+DRC+SC 0.986 0.993 0.935 0.940 OSEM+AC+DRC 0.972 0.930 0.956 0.907 OSEM+AC 0.951 0.907 0.944 0.825 OSEM+DRC 0.952 0.940 0.880 0.880 OSEM 0.841 0.955 0.886 0.889 FBP 0.929 0.978 0.896 0.857 Using the method described in section 5.3.2 Myocardial infarct size - Statistical analysis, the slopes of the different linear regression analysis plots were compared. Table 6.33 presents a chart of the significant difference between the slopes of each plot and unity, the ideal slope. Table 6.34 presents a chart of the significant difference between the slopes of the plots for different infarct locations. Table 6.33: Comparison of each slope of linear regression analysis and unity, the ideal slope. s for a significant difference and x for no significant difference (p=0.05). An x is therefore the ideal result for a good quantitative reconstruction technique. Reconstruction technique Inferior wall infarct Anterior wall infarct Lateral wall infarct Septal wall infarct OSEM+AC+DRC+SC </ X OSEM+AC+DRC X </ </ OSEM+AC X S X OSEM+DRC </ X </ </ OSEM FBP Chapter 6: Results and Discussion 122 Table 6.34: Comparison of the slopes of linear regression analysis between infarcts in different locations. S for a significant difference and x for no significant difference (p=0.05). An x is therefore the ideal result for a good quantitative reconstruction technique. Reconstruction technique Location of infarct Inferior and Anterior and Lateral and Anterior Lateral Septal Lateral Septal Septal OSEM+AC+DRC+SC S X •/ X OSEM+AC+DRC >/ X •/ X OSEM+AC V X X X OSEM+DRC X X OSEM </ X •/ FBP </ S X The effect of infarct location on the accuracy of its reconstructed size, was determined by calculating the absolute difference between the true infarct size and its measurement, averaged over all infarct sizes for each location. Results are presented in Table 6.35. Table 6.35: Absolute difference between the truth and the infarct size of the phantom determined from different reconstructions, averaged over small, medium and large infarcts. The stated errors are the Confidence Intervals of 95%. Reconstruction technique Absolute difference between the truth and the measured infarct size (% of total myocardium) Inferior Anterior Lateral Septal OSEM+AC+DRC+SC 1.26 ±0.36 0.49 ± 0.39 0.82 ±0.30 1.26 ±0.49 OSEM+AC+DRC 1.59 ±0.73 1.17 ±0.92 1.36 ±0.55 2.27 ±0.62 OSEM+AC 1.93 ± 1.23 1.32 ± 1.14 1.87 ±0.62 1.53 ± 1.32 OSEM+DRC 4.46 ± 1.22 1.22 ±0.70 2.39 ±0.32 3.03 ± 1.70 OSEM 4.25 ± 1.87 1.93 ±0.67 2.23 ±0.63 2.57 ± 1.65 FBP 3.43 ± 1.15 1.33 ±0.58 1.68 ±0.85 3.21 ± 1.96 A paired-sample t-test (p=0.05) was used to compare the measurement of myocardial infarct size with the truth for all infarct sizes. The OSEM+AC+DRC+SC reconstruction is the only technique that shows no significant difference between the measured values and the truth, for all infarct locations. Chapter 6: Results and Discussion 123 Preliminary results from this section were presented in poster form at the IEEE Medical Imaging Conference 2003 [202], and final results at the IEEE Medical Imaging Conference 2004 [210]. 6.4.2 Clinical data Thirteen of the clinical studies acquired from patients post Ml, were acquired with transmission data sets. Myocardial infarct size measurements of the OSEM+AC+DRC and FBP reconstructions of these data sets (performed using iQuant), are presented in Table 6.36. Also presented in this table are notes on the location of any infarct. Table 6.36: Myocardial infarct size measurements from OSEM+AC+DRC and FBP reconstructions of clinical data sets. Patient # Infarct size measurement (%) Infarct location notes* OSEM+AC+DRC FBP 1 17.5 21.7 inf 2 14.8 20.2 inf 3 15.4 33.6 ant 4 19.6 33.4 ant 5 0.0 8.0 inf 15 0.0 0.0 normal 16 0.0 16.6 inf 17 0.0** 0.0 ant 18 0.0 17.3 inf 19 0.0** 13.5 inf 20 0.0** 0 normal 21 20.5 26.5 inf 22 44.6 44.6 ant * Infarct location notes: inf = inferior wall infarct, ant = anterior wall infarct, normal = no infarct. Very small apical holes were visible in these data sets (0.9-2.8% of the total myocardium in size). Chapter 6: Results and Discussion 124 6.4.3 Discussion Phantom studies were used to determine the effect of different reconstruction techniques on the relative quantitation of myocardial infarct size. Using linear regression analysis to compare the measurements of infarct size with the true infarct size (known for a phantom experiment), a 'perfect' quantitative reconstruction technique would show a correlation coefficient of unity and a slope of unity. The reconstruction technique that produces the correlation coefficient closest to unity is OSEM+AC+DRC+SC for every infarct location, except the lateral wall where both the OSEM+AC+DRC and the OSEM+DRC reconstructions are closer. As can be seen from Table 6.31, the slope of the linear regression analysis of the OSEM+AC+DRC+SC reconstructions are closer to unity than any other reconstruction in every case except one (the OSEM+DRC is closer by 0.01 for the septal wall infarct). However, this observation is not found to be statistically significant (Table 6.33) for the following reason. It is noted that the error in the slope for the linear regression analysis of the OSEM+AC+DRC+SC reconstructions are generally smaller than those of other reconstructions. This indicates how well the 15 measurement points cluster around the best fit line. However, when looking at the significant difference between the slope of these lines and unity (the ideal value), the smallness of this error becomes an inhibiting factor. The results from other reconstruction techniques with slopes further from unity but with greater slope errors, show no significant difference to unity. However, the slope of the OSEM+AC+DRC+SC reconstruction, closer to unity but with a small error, shows a significant difference to unity. This point is illustrated with the comparison of Figure 6.16 and 6.20, the linear regression analysis of OSEM+AC+DRC+SC and OSEM reconstructions of the inferior wall infarcts. They clearly show the large slope and large error of the OSEM reconstruction, and the smaller slope and smaller error of the OSEM+AC+DRC+SC reconstruction. Another point of interest observable form Figures 6.16 and 6.20, is the more precise measurement of the larger infarct size by the OSEM+AC+DRC+SC reconstruction technique. The large spread in measurements taken of the large infarct by the OSEM reconstruction is also mirrored in the graphs prepared for the linear regression analysis of each of the other reconstruction techniques (Figures 6.17 to 6.21 and Appendix C). Although the partial volume effect around the edges of the myocardium and the boundaries between the viable and infarcted tissue plays a much greater role in the determination of small infarct volumes as opposed to larger ones; as the infarct increases significantly in size, the operator (or the software) will get less guidance on its location. This results in a loss of precision for large infarcts, which is reduced only by truly accurate reconstructions. The absolute difference between the true infarct size and its measurement was used to determine the effect of infarct location on the accuracy of infarct size (Table 6.35). Measurement of the anterior and lateral wall infarcts are consistent in accuracy for all reconstruction techniques. Measurement of the inferior and septal walls, which are positioned deeper into the body than the anterior and lateral walls, are more accurate when the reconstruction includes AC. The inclusion of DRC has no noticeable effect Chapter 6: Results and Discussion 125 on their accuracy. The OSEM+AC+DRC+SC reconstruction produces infarct sizes significantly closer to the truth than those measured from any other reconstruction technique. Data sets from clinical studies were also used to compare the size of infarcts reconstructed using FBP and OSEM+AC+DRC. In every case the inferior infarcts are smaller in size when measured from the OSEM+AC+DRC reconstruction than when measured from the FBP reconstruction (Table 6.36). In 4 out of 7 of these cases, the inferior infarcts are not even identifiable in the more comprehensive reconstruction. This phenomena is mainly due to the high attenuation of photons originating in the inferior myocardial wall. FBP does not correct for photon attenuation and therefore any infarct in the attenuated wall will appear larger in size, and a healthy attenuated wall may appear as if it contains an infarct. The phenomenon is further exaggerated in the presence of a liver with significant tracer uptake lying very close to the myocardium; which occurred in 3 out of the 4 cases when the inferior infarct of the FBP reconstruction was not identified in the OSEM+AC+DRC reconstruction. In these cases it is possible that the original appearance of the inferior wall infarct is due to the FBP reconstruction of the liver. In summary the diagnostic quantitation parameter of myocardial infarct size was used to compare different reconstruction techniques. OSEM+AC+DRC+SC is seen to determine the size of small to large myocardial infarcts more accurately and more precisely than other reconstruction techniques, and is able to determine the presence of very small infarcts. All reconstruction techniques determine a similar size for anterior and lateral wall infarcts, whereas inferior and septal wall infarcts, positioned deeper into the body, are more accurately determined from reconstructions that included AC. The inclusion of DRC has no noticeable effect on the determination of infarct size. The OSEM+AC+DRC+SC reconstruction is the only technique that shows no significant difference between the measured values and the truth, for all infarct locations. In clinical data sets, inferior wall infarcts are smaller in size when measured from OSEM+AC+DRC reconstructions than from FBP reconstructions. 126 C H A P T E R 7 C O N C L U S I O N S In the scope of this thesis SPECT corrections for photon attenuation, photon scatter and distance-dependent resolution loss, have been implemented both experimentally and in the clinical environment, and software has been developed to evaluate three clinical quantitative measurements. This work concludes that accurate quantitative information can be extracted from nuclear medicine studies. The iQuant software has been developed and successfully used to determine myocardial infarct size, myocardial wall thickness and the biodistribution of activity. It allows the extraction of fully 3-dimensional quantitative information (activity concentration and/or volume) from any data set. The main advantage of iQuant over the other myocardial quantitation software is the fact that it does not require the creation of a polar map. Polar maps are shown to overestimate the size of a myocardial defect in the presence of basal shortening of the septal wall, which is observed to be a normal occurrence in clinical studies. Additionally polar maps cannot detect thinning of the myocardium which is particularly important at the borders of an infarct, and for the detection and measurement of epicardial infarcts (infarcts that do not traverse the complete width of the myocardial wall). The threshold used to define viable myocardial tissue for iQuanfs measurement of myocardial infarct size depends on the reconstruction technique applied (50% for FBP, OSEM and OSEM+AC, 45% for OSEM+DRC and OSEM+AC+DRC and 35% for OSEM+AC+DRC+SC). Validation of the measurement of myocardial infarct size by iQuant shows very good inter-observer and intra-observer reliability, with a suggestion that intra-observer variation will improve further with the continued clinical training and experience of observers. With noiseless data sets iQuant is accurate to within an average of 0.3% of the total myocardial volume for a 15.4% myocardial infarct. The values of infarct size determined by iQuant for the solid insert phantom study, are comparable to those determined by the Mayo Clinic myocardial quantitation software. The results of the study of myocardial wall thickness show that the use of OSEM+AC+DRC as the routine clinical reconstruction algorithm will reduce the number of normal heart databases or thresholds required for quantitative myocardial analysis. Chapter 7: Conclusions 127 This work has shown that the comprehensive set of corrections for photon attenuation, photon scatter and distance-dependent resolution loss, developed at MIRG, significantly enhance the quantitative information gathered from clinical data sets, confirming the hypothesis set down at the beginning of this work. The relative importance of each SPECT correction has been evaluated. Results show that the inclusion of AC in the reconstruction technique significantly improves the accuracy of biodistribution estimates (reducing the relative difference between the true and estimated tumor activities by approximately 30%). The application of AC also improves the reconstruction of myocardial infarct sizes in both the inferior and septal walls (reducing the absolute difference between the true and measured myocardial infarct size to within 2% of the total myocardial volume), showing the removal of artefacts associated with these walls. However, AC increases myocardial wall thickness (by an average of 3mm), taking the values further from the truth, and thereby inhibiting any visual interpretation of the images. The inclusion of DRC to the reconstruction technique has no significant affect on the reconstruction of infarct sizes within the inferior or septal walls, or on the accuracy of biodistribution estimates unless AC is also performed (reducing the relative difference between the true and estimated tumor activities by a further 20%). The application of DRC does result in a smaller myocardial wall thickness (by an average of 5mm), providing a value closer to the truth, and enhancing visual interpretation of the images. The use of both AC and DRC is therefore essential to the accurate diagnostic assessment of myocardial perfusion studies. The visual accuracy of activity distribution in the images and a myocardial infarct size that can be estimated to within 2% of the total myocardial volume, are dramatic improvements on the present clinical situation. These factors provide a condition where clinical diagnosis is both easier and no longer ambiguous, as artefacts have been removed from the images. The use of both AC and DRC is also essential to the determination of biodistribution for dosimetry calculations (showing a relative difference between the true and estimated tumor activities of approximately 20%), however further correction is required. The addition of SC to the reconstruction process significantly improves the accuracy seen in the estimates of biodistribution, particularly in regions with non-uniform attenuation properties (reducing the relative difference between the true and estimated tumor activities to approximately 5% for tumors greater than 5ml in volume). The application of SC improves the accuracy of myocardial wall thickness (decreasing the value to an average of 2mm below that of OSEM+DRC, which is the next most accurate reconstruction in this respect). SC also improves the accuracy and precision of the reconstruction of myocardial infarct size, showing no significant difference from the truth for all infarct locations (reducing the absolute difference between the true and measured myocardial infarct size to an average of 0.75% of the total myocardial volume). The incremental visual enhancement of images and the more accurate measurement of myocardial infarct size achievable with SC in comparison to OSEM+AC+DRC, will not have a significant diagnostic impact on routine myocardial perfusion studies. The only exception to this may be when photons Chapter 7: Conclusions 128 originating in the liver are scattering in the inferior wall of the myocardium and disguising a suspected inferior wall infarct. In this case the application of SC during reconstruction may provide diagnostically significant results. The application of SC in addition to AC and DRC has been shown to consistently measure myocardial infarct size to within 5% of its true value. The accuracy of this measurement will have a significant impact on clinical trials using myocardial infarct size as an indication of patient mortality to determine the relative effectiveness of Ml treatments. The application of SC, AC and DRC has also been demonstrated to provide tumour activity measurement to within 5% of the truth irrespective of its position within the body. The accuracy of this measurement should have a significant clinical impact on nuclear medicine therapy and be especially important for therapeutic and diagnostic research. The OSEM+AC+DRC+SC reconstruction technique will continue to provide more accurate quantitative information, as both the statistical noise and the spatial resolution of SPECT data sets improve. Statistical noise will be reduced by the improving efficiency of gamma cameras and their collimators (the system sensitivity), and spatial resolution will be improved when increased computational power allows the reconstruction of 256x256 projections. However, more immediately, the recent advent of CT based attenuation maps will improve the spatial resolution of AC and SC, which will in its turn, improve the accuracy of SPECT quantitation. It should be noted however, that photon attenuation, photon scatter and distance-dependent resolution loss are not the only problems that degrade the accuracy of quantitative information gathered from nuclear medicine data sets. In particular, patient movement and the partial volume effect play a significant role. As patient movement is a very broad subject and thoughtful analysis would require significant additional work, this effect was not investigated in this thesis. The partial volume effect can be minimised using a matrix with smaller voxels, however this degrades the signal-to-noise ratio therefore a compromise has to be made. Although in this thesis the partial volume effect played a significant role in the poor measurement of myocardial wall thickness, its detrimental role was minimised by the use of detector response compensation in the reconstruction technique. Nuclear medicine studies from which quantitative information will be gathered, should not be undertaken without measures to restrict or monitor patient movement and without understanding of the possible implications of the partial volume effect. 129 C H A P T E R 8 F U T U R E W O R K The author believes that the conclusions drawn from this thesis should be implemented in the clinical and research environments. The future work of this thesis will therefore involve a transfer of knowledge to the technicians and clinicians who work in nuclear medicine. To this end, this research is being presented to the local nuclear medicine community and formatted for further international publication. 8.1 Improving, extending and developing experiments Firstly it should be noted that the methods used in this work to correct for photon attenuation, photon scatter and distance-dependent resolution loss, are only one set of the possible methods available. It is believed that each method used is one of the most advanced and accurate in its field. However, recently hardware has become available on the commercial market that allows the dual acquisition of CT and SPECT data sets, providing simple co-registration of a CT attenuation map into the SPECT reconstruction process. Due to the improved spatial resolution of the CT map, AC and SC will further increase in accuracy. Therefore, once the CT/SPECT hardware becomes available to MIRG, experiments should be repeated to study the affect of this improved attenuation map. Although the studies carried out on phantom and clinical data sets to determine myocardial wall thickness allowed the comparison of a number of variables commonly seen in the clinical environment, it was not possible to study all variables. It would therefore be interesting to develop phantom studies to investigate these additional variables that include the use of the isotope 201TI instead of the now more commonly used 9 9 m Tc, and the use of a general purpose collimator instead of a high resolution collimator. Due to the routine protocol used for myocardial perfusion studies in the nuclear medicine department at VGH, clinical data sets could not be used to investigate these or additional clinical variations. Enlarging the database to include other centres that might use alternative imaging protocols, would significantly increase the cost of assembling the database and would also encompass a number of other variations which would inhibit the comparison of data sets between hospital sites. Ideally, to provide a test that adheres as closely as possible to the clinical situation, a physical phantom should contain a beating heart. Several phantoms are available that in some way mimic the beating heart (some with and some without the surrounding thorax), however, none allow the inclusion of myocardial defects as the problems associated with this are presently too numerous. A useful dynamic cardiac phantom should encompass the following: Chapter 8: Future Work 130 • The perfusion defect should be connected to both the epi- and endo-cardiac surfaces to prevent shifting during the cardiac cycle. • When a region is poorly perfused its function is also inhibited leading to dyskinetic wall motion. This means that the defect would not be required to "beat" like the rest of the left ventricle. However, during the cardiac cycle the poorly perfused region changes shape as it is squashed and stretched by the surrounding myocardium, therefore the defect should not be a solid structure but made of a material that will deform under stress and stain. • Poorly perfused regions do take up some activity, so the defect should be hollow and have a strong but small valve that allows for the insertion and removal of activity, this would allow for a large range of clinical situations to be investigated. • It should be possible to mount the heart in various orientations around the base. The perfusion defect could therefore be positioned in the inferior, septal, anterior or lateral wall. Siemens are currently working alongside Data Spectrum Corp. to develop a Dynamic Cardiac Phantom that will allow the inclusion of perfusion defects, and the detailed remarks above are being considered in the design process by Hans Vija of Siemens. Once such a phantom has been developed, the experiments detailed in this work should be repeated, allowing for the physical analysis of a beating heart within a non-uniform attenuation thorax. Another improvement to the existing Thorax phantom would be the ability to insert an infarct into the apex of the myocardium. In the clinical environment infarcts are detected in this region and it is the only area that was not fully investigated in this work. The development of an apical defect and its use in experiments similar to those specified in this work, would result in a comprehensive set of results. 8.2 Mov ing iQuant in to the c l in ica l arena One of the ideal outcomes of this work would be to develop iQuant into a piece of software suitable for use in the clinical environment. It has several advantages over commercially available products and a number of disadvantages which could be overcome with the correct expertise. Advantages include its use of thresholds rather than normal heart databases each containing information from numerous patients with a low likelihood of coronary artery disease acquired on that specific camera. Its primary advantage however is the 3-D analysis, removing the need for a polar map which morphs and approximates the data sets into 2-D. Because of this 3-D analysis, the common clinical occurrence of a short septal wall, will have no affect on the accuracy of iQuant. iQuant can also detect myocardial thinning around the area of infarct and epicardial infarcts (infarcts that do not traverse the entire width of the myocardial wall). These things are not possible with polar maps. Disadvantages of iQuant include the inability to determine the severity of an infarcted or ischemic region. Although the boundary conditions required to delineate a defect into regions of varying severity were not determined in this work, as they were irrelevant to its outcome, they could easily be determined in a similar way to the original infarct boundary conditions. Once this information is known a Chapter 8: Future Work 131 severity indicator would be simple to add to the software and would enable full quantitative analysis of any infarcted or ischemic myocardial defect. The main disadvantage of iQuant however, is the extensive operator interaction presently required to determine the regions of myocardial defect. Although the inter- and intra-observer reliability was classified as very good, the extensive operator interaction means that the measurement of infarct size is a lengthy process. Automation would reduce the time required to an acceptable value, suitable for the measurement of numerous clinical studies. The automation of iQuant would firstly require the segmentation of the viable myocardium. The boundary condition threshold or a more advanced edge detection technique could be used in conjunction with shape recognition software to pick out the LV myocardium from other areas of significant activity such as the RV or the liver. This process is presently being investigated by a Masters student in the Department of Computer Science at the Otto-Von-Guericke-University, Magdeburg, Germany, under the supervision of Professor Klaus Toennies. The second issue to resolve before iQuant can be considered fully automated is the extension of the viable region to include the infarcted region. This can be done using an active contour model based on splines. Unlike linear interpolation where each sample point can be considered to be joined to the next point by a straight line, splines link the discrete points with a continuous function. To create a spline the function between sample points is described by a polynomial of degree n, and the functions are continuous at each sample point. Professor Ghassan Hamarneh of the School of Computer Science at Simon Fraser University, Burnaby, BC has developed an active contour model known as a snake. In 2-D, nodes (sample points) are positioned around a short axis slice of the LV, the algorithm then deflates the nodes drawing them in until they reach the LV and form the regular shape of the epi-cardial surface. Nodes positioned inside the LV can be inflated to locate the regular endo-cardial surface. Initial analysis shows the 2-D snake algorithm to accurately determine the location of the cardiac surfaces of short axis slices in the presence of an infarct. Further development of this algorithm into 3-D would provide the automation iQuant requires. Once iQuant is automated and can determine the presence of ischemic as well as infarcted regions, sensitivity and specificity studies should be carried out to establish its ability to detect true positive and true negative results, and hence its ability to perform in a clinical setting. These studies have not yet been carried out as the software was not designed to differentiate between regions of mild ischemia and viable myocardium, an ability that would be tested in sensitivity and specificity studies. iQuant was designed to determine the accuracy of reconstruction techniques, and to do this it was used to measure data sets generated from phantoms. The only situation when iQuant could not determine the presence of an infarcted region was in the case of the very small phantom infarct reconstructed with techniques not involving AC. It is believed that the inability to detect these regions was the fault of the reconstruction technique and not a lack of sensitivity in iQuant. Chapter 8: Future Work 132 8.3 The further investigation of liver activity It was found that the presence of a liver showing significant tracer uptake and lying close to the myocardium did not affect the reconstructed myocardial wall thickness, or the boundary condition threshold determined to detect viable myocardium for the more complex reconstruction techniques. However, the clinical data sets from patients with known Ml suggest that the presence of liver interference may cause problems in the identification of inferior wall infarcts either using FBP reconstruction or using reconstruction techniques involving just AC. The problems of liver interference are well known in the clinical setting and it was because of this that the development of iQuant included the creation of a Liver Removal program. It would be of great interest to further investigate the issue of livers, perhaps answering some of the following questions: Does the removal of the liver from a reconstructed data set provide a more accurate measure of myocardial infarct size on the physical phantom? Does the removal of the liver from a reconstructed data set make any statistical difference to the infarct sizes measured in clinical data sets? It would be possible to remove the liver from projection data sets using iQuant and therefore to reconstruct a data set without primary photons originating in the liver, would this have any affect on the reconstruction of infarct size? The answers to all these questions could be determined using a series of phantom studies involving a liver insert, and the clinical data sets already collected in the VGH database and not designated as having a < 5 % likelihood of CAD. 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Phys., 18(5), 1016-1024, 1991. 150 APPENDIX A A 1 : PARAMETER DETAILS FOR M C A T BODY 0 : activity_phantom_each_frame (1=save phantom to file, 0=don't save) 1 : activity_phantom_average (1=save , 0=don't save) 0 : attenuation_coeff_phantom_each_frame (1=save , 0=don't save) 1 : attenuation_coeff_phantom_average (1=save, 0=don't save) 0 : motion_option (0=heart only, 1=resp only, 2=heart and resp) 1 : output_period (SECS) 0 : internal_frames (to generate within time frame motion = 0 ignore) s -1 : seed - random location of lungs during cardiac gating (integer and < 0 ) 1 : time_per_frame (SECS) (**IGNORED unless output_period<=0**) 1 : output_frames (# of output time frames ) 1 : hrt_period (SECS) (length of beating heart cycle; normal = 1s) s 0.0 : hrt_start_phase_index (range=0 to 1; ED=0, ES=0.3516) 5 : resp_period (SECS) (length of respiratory cycle; normal breathing = 5s) 0.0 : resp_start_phase_index (range=0 to 1, full exhale=0, full inhale=0.455) 2.0 : max_diaphragm_motion (CM) (normal breathing = 2 cm) 0.2 : max_saxis_exp (CM) (max rib/body short axis expansion; normal = 1 cm) 0.0 : max_laxis_exp (CM) (max rib/body long axis expansion; normal = 0.0 cm) 0 : heart translation due to diaphragm motion (0=linear, 1=base rotation) 1.0 : hrt_scale (1.0 is ave. male; realistic range : 0.8 to 1.2) 0 : breast_type (0=supine, 1=prone) 1 : which_breast (0 = none, 1 = both, 2 = right only, 3=left only ) 1 : right_diaphragm/liver position (0=NOT raised, 1=raised) 0 : left diaphragm position (0=NOT raised, 1=raised) 0 : arm(s) present (0 = none, 1 = right arm only , 2 = both arms) 0.6 : intv in cm (thickness of body tissue around the heart and liver) 0.4795 : pixel width (cm) 128 : array size (should not exceed 256) Appendix A 2 : subvoxel_index (=1,2,3,4 -> 1,8,27,64 subvoxeis/voxel, respectively) 1 : start_slice 128 : end_slice 1 : increment between slices -110 : zy_rotation (beta) in deg. 23. : xz_rotation ( phi) in deg. -52. : yx_rotation ( psi) in deg. 3.0 : x translation in cm -1.2 : y translation in cm -2.00 : z translation in cm 0.2 : apical_thin_fraction (range:0 to 1, 0=no thinning) 1.0 : apical thin, Y dim adjustment 1.0 : apical thin, Z dim adjustment 0.1 : valve thickness in cm (0= no valve) 0.1 : av_step(cm): step width for smooth change between Atr & Ven (0=none) 0.0 : total wringing (deg) 0 : activity units (1= scale by voxel volume; 0= don't scale) 0 : hrt_myoLV_act - activity in left ventricle myocardium 0 : hrt_myoRV_act - activity in right ventricle myocardium 0 : hrt_myoLA_act - activity in left atrium myocardium 0 : hrt_myoRA_act - activity in right atrium myocardium 10 : hrt_bldplLV_act - activity in left ventricle chamber (blood pool) 10 : hrt_bldplRV_act - activity in right ventricle chamber (blood pool) 10 : hrt_bldplLA_act - activity in left atria chamber (blood pool) 10 : hrt_bldplRA_act - activity in right atria chamber (blood pool) 10 : body_activity (background activity) 0 : liver_activity 5 : lung_activity 10 : st_wall_activity (stomach wall) 10 : st_cnts_activity (stomach contents) 10 : kidney_activity 10 : spleen_activity 10 : rib_activity 10 : spine_activity Appendix A 152 A 2 : P A R A M E T E R D E T A I L S F O R M C A T H E A R T 0 : activity_phantom_each_frame (1=save phantom to file, 0=don't save) 1 : activity_phantom_average (1=save , 0=don't save) 0 : attenuation_coeff_phantom_each_frame (1=save , 0=don't save) 1 : attenuation_coeff_phantom_average (1=save, 0=don't save) 0 : motion_option (0=heart only, 1=resp only, 2=heart and resp) 1 : output_period (SECS) 0 : internal_frames (to generate within time frame motion = 0 ignore) s -1 : seed - random location of lungs during cardiac gating (integer and < 0 ) 1 : time_per_frame (SECS) (**IGNORED unless output_period<=0**) 1 : output_frames (# of output time frames) 1 : hrt_period (SECS) (length of beating heart cycle; normal = 1s) s 0.0 : hrt_start_phase_index (range=0 to 1; ED=0, ES=0.3516) 5 : resp_period (SECS) (length of respiratory cycle; normal breathing = 5s) 0.0 : resp_start_phase_index (range=0 to 1, full exhale=0, full inhale=0.455) 2.0 : max_diaphragm_motion (CM) (normal breathing = 2 cm) 0.2 : max_saxis_exp (CM) (max rib/body short axis expansion; normal = 1 cm) 0.0 : max_laxis_exp (CM) (max rib/body long axis expansion; normal = 0.0 cm) 0 : heart translation due to diaphragm motion (0=linear, 1=base rotation) 1.0 : hrt_scale (1.0 is ave. male; realistic range : 0.8 to 1.2) 0 : breast_type (0=supine, 1=prone) 1 : which_breast (0 = none, 1 = both, 2 = right only, 3=left only ) 1 : right_diaphragm/liver position (0=NOT raised, 1=raised) 0 : left diaphragm position (0=NOT raised, 1=raised) 0 : arm(s) present (0 = none, 1 = right arm only , 2 = both arms) 0.6 : intv in cm (thickness of body tissue around the heart and liver) 0.4795 : pixel width (cm) 128 : array size (should not exceed 256) 2 : subvoxeMndex (=1,2,3,4 -> 1,8,27,64 subvoxels/voxel, respectively) Appendix A 153 1 : start_slice 128 : end_slice 1 : increment between slices -110 : zy_rotation (beta) in deg. 23. : xz_rotation ( phi) in deg. -52. : yx_rotation ( psi) in deg. 3.0 : x translation in cm -1.2 : y translation in cm -2.00 : z translation in cm 0.2 : apical_thin_fraction (range:0 to 1, 0=no thinning) 1.0 : apical thin, Y dim adjustment 1.0 : apical thin, Z dim adjustment 0.1 : valve thickness in cm (0= no valve) 0.1 : av_step(cm): step width for smooth change between Atr & Ven (0=none) 0.0 : total wringing (deg) 0 : activity units (1= scale by voxel volume; 0= don't scale) 40 : hrt_myoLV_act - activity in left ventricle myocardium 20 : hrt_myoRV_act - activity in right ventricle myocardium 10 : hrt_myoLA_act - activity in left atrium myocardium 10 : hrt_myoRA_act - activity in right atrium myocardium 0 : hrt_bldplLV_act - activity in left ventricle chamber (blood pool) 0 : hrt_bldplRV_act - activity in right ventricle chamber (blood pool) 0 : hrt_bldplLA_act - activity in left atria chamber (blood pool) 0 : hrt_bldplRA_act - activity in right atria chamber (blood pool) 0 : body_activity (background activity) 0 : liver_activity 0 : lung_activity 0 : st_waInactivity (stomach wall) 0 : st_cnts_activity (stomach contents) 0 : kidney_activity 0 : spleen_activity 0 : rib_activity 0 : spine_activity 140. : radionuclide energy in keV (range 1-1000 keV) for attn. map only Appendix A 154 A3: P A R A M E T E R D E T A I L S F O R M C A T M Y O C A R D I A L I N F A R C T S Where: theta_center: location of lesion center in circumferential dimension theta_width : lesion width in circumferential dimension x center: lesion center in long-axis dimension x width: lesion width in long-axis dimension Medium inferior infarct 180.0 : theta center in deg. (between -180 and 180) 90.0 : theta width in deg., total width (between 0 and 360 deg.) 0.5 : x center (0.0=base, 1.0=apex, other fractions=distances in between) 0.5 : x width, total (between 0 and 1.0, 1.0=entire length of LV) Medium anterior infarct 0.0 : theta center in deg. (between -180 and 180) 90.0 : theta width in deg., total width (between 0 and 360 deg.) 0.5 : x center (0.0=base, 1.0=apex, other fractions=distances in between) 0.5 : x width, total (between 0 and 1.0, 1.0=entire length of LV) Medium lateral infarct 90.0 : theta center in deg. (between -180 and 180) 90.0 : theta width in deg., total width (between 0 and 360 deg.) 0.5 : x center (0.0=base, 1.0=apex, other fractions=distances in between) 0.5 : x width, total (between 0 and 1.0, 1.0=entire length of LV) Medium septal infarct -90.0 : theta center in deg. (between -180 and 180) 90.0 : theta width in deg., total width (between 0 and 360 deg.) 0.5 : x center (0.0=base, 1.0=apex, other fractions=distances in between) 0.5 : x width, total (between 0 and 1.0, 1.0=entire length of LV) Appendix A 155 Small inferior infarct 180.0 : theta center in deg. (between -180 and 180) 45.0 : theta width in deg., total width (between 0 and 360 deg.) 0.5 : x center (0.0=base, 1.0=apex, other fractions=distances in between) 0.5 : x width, total (between 0 and 1.0, 1.0=entire length of LV) Large inferior infarct 180.0 : theta center in deg. (between -180 and 180) 180.0 : theta width in deg., total width (between 0 and 360 deg.) 0.5 : x center (0.0=base, 1.0=apex, other fractions=distances in between) 0.5 : x width, total (between 0 and 1.0, 1.0=entire length of LV) Very large inferior infarct 180.0 : theta center in deg. (between -180 and 180) 180.0 : theta width in deg., total width (between 0 and 360 deg.) 0.5 : x center (0.0=base, 1.0=apex, other fractions=distances in between) 1.0 : x width, total (between 0 and 1.0, 1.0=entire length of LV) 156 A P P E N D I X B B 1 : O P E R A T I N G I N S T R U C T I O N S F O R IQUANT D O S I M E T R Y Reading in Data • In the Matlab environment, start imagetools. • Under the File menu, Open file. e TooK iQumi 6*»mpl* Took MIRG ImageTools O p e n e d F i l e s O p e n e d Images C l o s e F i l e j C l o s e linage Figure B1.1: Main window. /nfs/kdi ' f e ^ d i x o n / d o s i m e t r y /p hantoms reconstructions (BLANK SCAN.HDR (BLANK SCAN. IMG CALIB_AC.HDR jCALIB AC.IMG ]JAZ_AC.HDR JAZ AC.IMG MU CALIB.HDR MU_.CALIB.IMG IMU JAZ.HDR Open File of Type: '.niirg User Definable Title, j Select a file. Filter Type: butterworth Cutoff. Ksize: 0.55 Order, Width: 5 4 Mir (rtlv&te by s?) I Figure B1.2: Open file window. • Select the file of interest using the .. in the file list to navigate between directories. • Using the hidden menus select: o File type o Spatial filter o Toggle the FBP button if the reconstruction was FBP. • Open the file. Dosimetry • Under iQuant menu, choose Tumor Dosimetry. • By clicking on the two images, move the cursor to a region of background. • Save coordinates of background, this will activate the iQuant button. • Enter iQuant. Appendix B D m a <§ t A /> • >« F " Tftte: tbor_*c X coord: 64 V coord: ao Z coord 25 Save coordinates ol background or tui Figure B1.3: Dosimetry region selecting window. • Toggle the Background measurement button. • Move to the Next page. Apply to I.IUJC :k_p»oe_ | Figure B1.4: Dosimetry threshold window. Appendix B 158 • Draw background VOI: o Toggle on Apply to All o Draw area o Move to another dimension o Toggle on Apply to All o Remove exterior to define VOI limits o Check VOI in third dimension Figure B1.5: Dosimetry display window - background VOI. • Once background VOI is satisfactory, Save VOI. • Click on VOI Information. • Select the required background VOI (if more than one VOI was saved) and note the Mean counts in the background region. • Close the Information box. • Finish the dosimetry window. Appendix B 159 V0I2 Close | Figure B1.6: Dosimetry VOI information box. • Return back to Tumor Dosimetry via the iQuant menu. • This time centre the cursor on the tumor, save the coordinates and enter iQuant. • Enter 2 times the mean value of the background VOI into the Tumor threshold box. • Enter 1.5 times the mean value of the background VOI into the Outline threshold box. • Click on Apply to Image and the threshold ed image will appear. • Move to Next page. • Auto Select VOI to include all voxels with values above the tumor threshold in a VOI. • Toggle Apply to All and use Remove Exterior to delete any sections of VOI that do not contain tumor. • This may be required in more than one dimension. Draw VOI ' Save VOI Lo.4d VOI Fi Next/Back page VOI lirfomiatai Figure B1.7: Dosimetry display window - tumor VOI. Appendix B • Draw VOI to check the VOI contains only tumor. • The surface rendered plot can be rotated and viewed from any angle. file Edit View j m M Tools Window H»ip Dt*B«d k A /• / 0 0^ Figure B1.8: Surface rendering of tumor VOI. • Once the tumor VOI is satisfactory, Save VOI. • Click on VOI Information. • Note the total number of counts in the VOI and its volume. Appendix B 161 B2: O P E R A T I N G I N S T R U C T I O N S F O R IQUANT M Y O C A R D I A L M E A S U R E M E N T Reading in Data • As described in Appendix B1: Operating Instructions for iQuant Dosimetry. Myocardial Measurement • Under iQuant menu, choose Myocardial Measurement. • By clicking on the two images, move the cursor to the centre of the left ventricle (LV). If wall thickness measurement are going to be taken, then the positioning of the cursor half way between apex and base is most important. IMIIIIIIMMMMJ w 1 Figure B2.1: Cursor placed in centre of left ventricle. • Save Cardiac Coordinates, a check button will appear. • Move the cursor to the myocardium and click on Find max count in cardiac. • In the new dialogue box click on Find max count in cardiac. Region Growing Parameters: W Diagonal Neighbours J Minimum Value: (379677 Maximum Value: 8.9354 Find max count in cardiac Figure B2.2: Cursor placed in myocardium. Figure B2.3: 3D region growing box. Appendix B 162 • A surface rendered plot will appear. • Check that only the LV has been included. If the plot is larger than the LV, repeat the last 3 steps increasing the Minimum Value in the dialogue box. • Enter iQuant. Figure B2.4: Surface rendering of (a) myocardium and liver, (b) myocardium alone. For infarct size measurement • Using the following Viable Threshold values: o 35% for OSEM+SC+AC+DRC o 45% for OSEM+AC+DRC and for OSEM+DRC o 50% for OSEM+AC and for OSEM and for FBP • Select an Outline Threshold that will complete the LV if it is not already complete. • Click on Calculate Thresholds. • Accept Thresholds. For wall thickness measurement • Use a suitable Viable Threshold value: either repeat these steps using variable thresholds or use the infarct size thresholds specified above. • Select an Outline Threshold with a value below the Viable Threshold (this value is not important but the program needs an input here to run correctly). • Click on Calculate Thresholds. • Accept Thresholds. Appendix B ThfC»i>old P»t»nictct» Acccpt/CKuigc Thresholds Figure B2.5: iQuant threshold window. For infarct size measurement • Pick the dimension to view the short axis of the LV. • Use Auto Select VOI to define a VOI around the viable threshold. Load VOI I F.mshed Acccpt'Clxnge Thf ejholdf Figure B2.6: iQuant display window. Appendix B 1 6 4 • Toggle on Apply to All. • Using Remove Exterior, draw around the LV taking care to separate the LV from any high external activity such as the liver. • Toggle through the slices containing the LV and use Add/Remove Voxels to remove any voxels presently contained in the VOI that are not LV voxels. • Draw VOI and view the surface rendered plot from all directions to ensure the VOI contains the LV only. • Save VOI. This is the Incomplete VOI containing only voxels with activity above the viable threshold. Figure B2.7: Surface rendering of viable myocardium VOI. • Now toggle through the slices again and using Add/Remove Voxels or Draw Area, add into the VOI areas of the LV that are under-perfused. To aid you in this process use your knowledge of cardiac anatomy, the thickness and shape of the well-perfused myocardium, and the outline threshold. • View each slice in each dimension to ensure the VOI is a true model of the complete LV. • Draw VOI and view the surface rendered plot from all directions to ensure the VOI contains the complete LV. • Save VOI. This is the Complete VOI containing the entire LV. Appendix B 165 • Once both VOIs are satisfactory, Compute VOI Difference. • Select the correct Complete and Incomplete VOIs (numbered in chronological order of saving). • Compute. Choose the Complete VOI VOI2 osc the Incomplete VOI von Compute Figure B2.9: VOI information select box. • A surface rendering of the two VOIs overlaid on each other will appear (viable LV in brown and infarct in green), together with a box providing information on the infarct (the difference between the two VOIs). Appendix B 166 Number of Pixels in Defect: 258 Number of Pixels in Complete Myocafdium: 2125 Size of Defect: 12.1412% Volume: 28.4437 ml Mean: 5.3211 Standard Deviation: 0.77208 Maximum Value: 8.6092 Minimum Value: 2.8928 Figure B2.10: VOI information box. fjla fcdst V-i*w SHert fgaH Wirrfsw H#ip Figure B2.11: Surface rendering of viable myocardium and infarct. Appendix B 167 For wall thickness measurement • Pick the dimension to view the short axis of the LV. • Use Auto Select VOI to define a VOI around the viable threshold. • Click on Add/Remove Voxels. This will produce a visible dot in the centre of all voxels contained in the VOI. • Move the cursor to the centre of the LV but do not click any mouse buttons. • Using the lines extending from the cursor to indicate the centre of each LV wall, note each wall's thickness (in voxels) at these points. • Click on the right mouse button to deactivate. • Using the Next Slice button, proceed 3 slices towards the apex. • Repeat the wall thickness measurement for this slice. • Using the Previous Slice button, proceed 6 slices towards the base. • Repeat the wall thickness measurement for this slice. • If another viable threshold is to be investigated, return to the threshold input page by clicking on Accept/Change Thresholds. Appendix B 168 B3: A D D I T I O N A L G E N E R A L I N S T R U C T I O N S F O R IQUANT MIRG ImageTools: Ft!* im&_$ Toots. iQuant Examptg Tool* j MIRG ImageTools Opened Fi les O p e n e d Images — N . t . - " " » --N< lil' Close File Close Image Figure B3.1: Main window. File menu: Open File: to select the file of interest, specifying its format type and the spatial filter (if any) to be applied to the data set. Open Images/View Files: to view the slices of the data set (in each of the 3 dimensions) and save any individual slice of interest for further analysis. Use default: File Type: specifies the file type used as default during Open File. Choices are *.rec *.mum *.mat *.mirg. Filter: if toggled off the default setting for Open File will be for no spatial filter, if toggled on the default setting will include a Butterworth filter with a cut-off of 0.55 and an order of 5. Send File to workspace: saves an opened file to the Matlab workspace. Send Images to Workspace: saves open images to the Matlab workspace. Image Tools menu: Image Difference Tool: compares an image to the corresponding true data set (for MCAT phantom and SIMSet simulations only). Appendix B 169 Profile Tool: draws an amplitude plot along a specified line through an image. A Gaussian fit can be applied to this plot. FFT Profile: performs a Fast Fourier Transform of the 2D image and displays it on either a SemiLog Y-axis or a Linear Y-axis. Display Selected Images: Interpolated Images: displays selected images using a simple interpolation. Images can be displayed on the Same Scale as each other, or on Individual Scales. Pixel Images: displays selected images in their original form. Images can be displayed on the Same Scale as each other, or on Individual Scales. Alter Selected Images: manipulates the selected 2D images using a flip - Flip Horizontal or Flip Vertical, or a rotation - Rotate 90 CCW or Rotate 90 CW. iQuant menu: Myocardial Measurement: starts iQuant for the purpose of measuring myocardial infarct size or left ventricle wall thickness. Liver Removal: starts iQuant for the purpose of removing obstructing activity from the vicinity of the myocardium. Tumor Dosimetry: starts iQuant for the purpose of measuring the activity within a tumor. Interpolate Data: interpolates the 3D data set onto a matrix 8 times the size of the original (2 times each dimension). Cubic or Linear interpolation can be carried out. Appendix B 170 iQuant Set-up Hef***f» <>*»!*« f I H»r*»» C#***«* 5 Figure B3.2: Region selecting window. The exact look of this window will depend upon the program used to enter it. Cursor: the position of the cursor is specified by a left mouse button click, or by the input boxes labelled X coord, Y coord and Z coord. Save coordinates of cardiac centre: saves the coordinates of the cursor. When complete the word 'Done' appears under the check list. Find max count in cardiac: starts the 3D region growing program which outputs the maximum count in the myocardium (average of the 30 highest amplitude voxels). When complete the word 'Done' appears under the check list. By default the program uses a threshold to define the outer limits of the region, alternatively the relationship between neighbouring voxels can be used by selecting 3D Region Growing by Relationship under the Region Selecting Tools menu. If the max count is already known, the value can be added to the input box next to the button. Third Dim., etc: each image has a dimension selector to allow all 3 dimensions to be viewed if necessary. Colourbar slider: used to change the colour scale of the image. Refresh Colourbar: changes the scale of the colourbar to match that of the image. Appendix B 171 iQuant or Remove Liver: enters the next section of iQuant. This button only appears once the coordinates have been entered and the max counts found (if applicable). Threshold Selection Figure B3.3: Threshold window. The exact look of this w indow will depend upon the program used to enter it. Colourmap menu: selects the colour map to be used for the remainder of the iQuant process. Save Properties menu: options for the behaviour of iQuant, toggle on to make the option active. Choices are Display VOI on Exit, Display Info on Exit, Output Saved to Workspace, Clear VOI after Save. Display image with Thresholds: by default this button is toggles on, al lowing the segmentat ion of myocardium or tumor by threshold. Toggle off this button if a background VOI is required and the data set will be displayed in its original colour scale. This will also disable all threshold related buttons. Threshold Parameters: for myocardial applications the max count in the myocard ium detected in the previous window appears as Counts in max voxels. Viable and Outline thresholds are input as a percentage, with default values of 5 0 % and 3 0 % which can be changed if necessary. For dosimetry applications Tumor and Outline thresholds are input by the user in counts/voxel . Appendix B 1 7 2 Calculate Thresholds: displays the central data set slice in 3 colours, one for voxels containing counts below the lower threshold, one for voxels between the 2 thresholds and one for voxels above the upper threshold. Size of working image: defines the dimensions of the displayed data set (zoomed in around the myocardium or tumor). If, when the Calculate Threshold button is pressed, a complete image is not seen, reduce these values in even steps and recalculate the threshold (reducing the Dim.3 value often has the desired effect). Accept/Change Thresholds or Next/Back page: moves to the next window. iQuant main page Figure B3.4: Display window. The exact look of this window will depend upon the program used to enter it. Colourmap menu: selects the colour map to be used for the remainder of the iQuant process. Line Colour menu: changes the colour of the lines used to delineate VOI. Save Properties menu: options for the behaviour of iQuant, toggle on to make the option active. Choices are Display VOI on Exit, Display Info on Exit, Output Saved to Workspace, Clear VOI after Save. Thumbnail images: show the position of the slice displayed in the main image. Appendix B 173 First Dim.: displays a different dimension of the data set. Auto Select ROI: defines a ROI encompassing all voxels with counts above the upper threshold in the viewed slice (2D). Auto Select VOI: defines a VOI encompassing all voxels with counts above the upper threshold in the displayed data set (3D). Polygon: the default setting for all drawing tools. Circular, square or oval ROIs can be defined by changing this option. Draw Area: draws an area which will define or add to a ROI. Left click to define a point on the polygon, right click to close the polygon. Apply to All: when toggled on the Draw Area, Erase Area, Remove Exterior and Clear Selection functions will apply to every slice of the displayed data set, changing an ROI tool into a VOI tool. Erase Area: draws an area which will be erased from a ROI. Left click to define a point on the polygon, right click to close the polygon. Remove Exterior: draws an area outside of which the ROI will be erased. Left click to define a point on the polygon, right click to close the polygon. Clear Selection: removes the entire ROI. Add/Remove Voxels: draws a point in the centre of all voxels contained in the ROI, left click on a voxel to add or remove it from the ROI, right click to exit the function. Zoom: zooms into the image with a left click and backs out of the image with a right click. Draw VOI: draws a surface rendered plot of the present VOI. The plot can be rotated and viewed from any angle. Save VOI: saves the present VOI. Find Pixel Value: displays the position and counts within the voxel defined with a left click. Right click over the image exits the function. Previous Slice/Next Slice: toggles through the slices of the displayed data set. Load VOI: loads a previously saved VOI (see next section). Finished: exits the iQuant program, returning to the original ImageTools window. Accept/Change Thresholds or Next/Back page: moves to the previous (threshold defining) window. Compute VOI Difference: computes the difference between 2 VOIs. Only activated if 2 or more VOI have been saved. Or Remove Liver: removes the liver from the data set, replacing it with counts equivalent to the background activity. Only activated if at least 1 B/G and one Liver VOI have been saved. Or VOI Information: displays information relating to a saved VOI. Only activated if 1 or more VOI have been saved. Appendix B 174 Loading VOIs Figure B3.5: VOI loading window. Save Properties menu: options for the behaviour of iQuant, toggle on to make the option active. Choices are Display VOI on Exit, Display Info on Exit, Output Saved to Workspace, Clear VOI after Save. Information on the present VOI is displayed. VOI -1 : lists the saved VOIs. Left click on a VOI to display it. Load old VOIs: input the Matlab workspace name of a previously saved set of VOIs and click on the button. These VOIs will be added to the list after the VOIs saved from the present data set. Accept: returns to the previous page with the selected VOI. Cancel: returns to the previous window with the original VOI. Appendix B 175 B4: OPERATING INSTRUCTIONS FOR IQUANT LIVER REMOVAL Reading in Data • As described in Appendix B1: Operating Instructions for iQuant Dosimetry. Liver Removal • Under iQuant menu, choose Liver Removal. • By clicking on the two images, move the cursor to the centre of the left ventricle (LV). Figure B4.1: Cursor placed in centre of left ventricle. • Save coordinates of cardiac centre, a check button will appear. • Move the cursor to the myocardium and click on Find max count in cardiac. • In the new dialogue box click on Find max count in cardiac. Region Growing Parameters: Minimum Value: ;3.9677 Maximum Value: #".'9354 Find max count in cardiac Figure B4.2: Cursor placed in myocardium. Figure B4.3: 3D region growing box. Appendix B 176 • A surface rendered plot will appear. • Check that only the LV has been included. If the plot is larger than the LV, repeat the last 3 steps increasing the Minimum Value in the dialogue box. Figure B 4 . 4 : Surface rendering of (a) myocardium and liver, (b) myocardium alone. • Enter Liver Removal. • Using the default thresholds of 50% and 20%, click on Calculate Thresholds. • Accept Thresholds. Figure B 4 . 5 : Liver removal threshold window. Appendix B 1 • Use Auto Select VOI to define a VOI around the lower threshold. • Toggle on Apply to All. • Using Erase Area, draw around the lower threshold of the left ventricle (LV). • Toggle through the slices to ensure that the VOI contains liver, gut, right ventricle etc, but not LV. • Save Liver VOI. • Toggle on Apply to All and use Clear Selection to remove the VOI. • Draw background VOI: o Toggle on Apply to All o Draw area o Move to another dimension o Toggle on Apply to All o Remove exterior to define VOI limits o Check VOI in third dimension • Save B/G VOI. Figure B4.6: Liver removal display window. Appendix B 1 7 8 • When both VOI are satisfactory, click on Remove Liver. • Select the correct VOI if more than one liver or background VOI was saved. • Click on Remove Liver Choose the Liver VOI Liver VOI1 Choose the Background VOI B/G VOI2 Remove Liver Figure B4.7: Liver removal VOI selection box. • Two images will appear, the original image and the image with the liver VOI removed and replaced by counts equivalent to background. • Use Previous Slice and Next Slice to toggle through the images. • If the images are satisfactory, Save data set to workspace and desktop. A .mirg format file with the prefix RemovedJJver will be saved to your present working directory. The data set will also be saved to the Matlab workspace. Appendix B Choose the Liver VOI Liver VO1 1 Choose the Background VOI BIG VOI2 Remove Liver Original Data: • * * g i o u r i d VOi *r Data v\h Liver Removed. to w Mop Figure B4.8: Liver removal output window. I 180 APPENDIX C ADDITIONAL GRAPHS FOR MYOCARDIAL INFARCT SIZE ANALYSIS OF PHANTOM DATA 20 18 16 14 12 10 8 6 4 2 0 1 y = 0.9283x + 0.9317 R2 - 0.9925 10 True infarct size (%) 15 20 Figure C.1: Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. 25 — 20 N '</) O 1_ -5 c 15 •D 0) i— 3 (A re a> 10 y = 0.9012x + 0.7616 R2 = 0.9304 • 10 True infarct size (%) 15 20 Figure C.2: Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 181 25 20 N * 15 o> 2 10 I y =0.8332x + 1.2831 R2 = 0.907 • 10 True infarct size (%) 15 20 Figure C.3: Linear regression analysis carried out on OSEM+AC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Figure C .4: Linear regression analysis carried out on OSEM+DRC reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 182 18 16 14 12 10 8 6 4 2 0 I y = 0.7656X + 0.8372 R2 = 0.9552 10 True infarct size (%) 15 20 Figure C.5: Linear regression analysis carried out on OSEM reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Figure C.6: Linear regression analysis carried out on FBP reconstruction of the anterior wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 183 O-l 1 1 1 1 0 5 10 15 20 True infarct size (%) Figure C.7: Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Figure C.8: Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 184 2 10 I y = 0.7738X + 0.9865 R2 = 0.9436 0 5 10 15 True infarct size (%) Figure C.9: Linear regression analysis carried out on OSEM+AC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Figure C.10: Linear regression analysis carried out on OSEM+DRC reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 185 16 14 0) N 12 uj +-> o 10 infa i 8 •a a> 6 3 <0 4 re 0) E 2 I y - 0.5346X + 4.8205 R2 = 0.8863 10 True infarct size (%) 15 20 Figure C.11: Linear regression analysis carried out on OSEM reconstruction ofthe lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Figure C.12: Linear regression analysis carried out on FBP reconstruction of the lateral wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 186 0 + - 1 1 1 1 0 5 10 15 20 True infarct size (%) Figure C.13: Linear regression analysis carried out on OSEM+AC+DRC+SC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. 0) E 2 0 5 10 15 20 True infarct size (%) Figure C.14: Linear regression analysis carried out on OSEM+AC+DRC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 187 CH 1 1 1 1 0 5 10 15 20 True infarct size (%) Figure C.15: Linear regression analysis carried out on OSEM+AC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Figure C.16: Linear regression analysis carried out on OSEM+DRC reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. Appendix C 188 35 0 5 10 15 20 True infarct size (%) Figure C.17: Linear regression analysis carried out on OSEM reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. 35 0 5 10 15 20 True infarct size (%) Figure C.18: Linear regression analysis carried out on FBP reconstruction of the septal wall infarct in the phantom. The legend presents the equation of the linear regression slope and the correlation coefficient R2. 

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