AUTOMATED PET/CT REGISTRATION FO R ACCURATE RECONSTRUCTION OF PET IMAGES By Khawar Khurshid A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering Doctor of Philosophy 20 1 8 ABSTRACT AUTOMATED PET/CT REGISTRATION FO R ACCURATE RECONSTRUCTION OF PET IMAGES By Khawar Khurshid The use of a CT attenuation correction (CTAC) map for the reconstruction of PET image can introduce attenuation artifacts due to the potential misregistration between the PET and CT data. This misregistration is mainly caused by patient motion and physiolog ical movement of organs during the acquisition of the PET and CT scans. In cardiac exams , the motion of the patient may not be sign ificant but the diaphragm movement during the respiratory cycle can displace the heart by up to 2 cm along the long axis of the body. This shift can project the PET heart onto the lungs in the CT image, thereby producing an underestimated value for the at t enuation. In brain studies, patients undergoing a PET scan are often not able to follow instructions to keep their head in a still position, resulting in misregistered PET and CT image datasets. The head movement is quite significant in m any cases despite the use of head restraints. This misaligns the PET and CT data, thus creating an erroneous CT attenuation correction map. In such cases , bone or air attenuation coefficients may be projected onto the brain which causes an overestimation or an underestimati on of the resulting CTAC value s . To avoid misregistration artifact s and potential diagnostic misinterpretation, automated software for PET/CT registration has been developed that works for both cardiac and brain datasets. This software segments the PET and CT data, extracts the brain or the heart surface information from both datasets , and compensates for the translational and rotational misalignment between the two scans. The PET data are reconstructed using the aligned CTAC, and the results are analyzed a nd compared with the original dataset. This procedure has been evaluated on 100 cardiac and brain PET/CT data sets , and the results show that the artifacts due to the misregistration between the two modalities are eliminated after the PET and CT images are aligned . iv Dedicated to my parents v ACKNOWLEDGEMENT S Firstly, I am very grateful to m y thesis advisor Dr. Robert. J. McGough , for his able guidance, encouragement , and advice throughout the course of my thesis . He has not only been an exceptional supervisor but a lifetime mentor for me . When ever I ca me across any difficulty , he was always there to help with an unmatched patience . It is hard to overstate my gratitude to him and his constant support without which I would have nev er been able to complete this work. I have been extremely lu cky to have him as my thesis advisor . I would als o like to thank Dr. Kevin Berger for his support and prompt response to all the queries and problems faced during this research. His expert knowled ge and all the clinical support allowed me to carry out the inter - departmental research smoothly. He was always available to help and provide insightful suggestions for the development of the software application. I am thankful to my committee membe rs Dr. Ramakrishna Mukkamala, Dr. Lalita Udpa , and Dr. Kyle Miller for their helpful advice and critical comments . I am also thankful to my lab mates and all my friends for constant motivation and inspiration, both professionally and personally. I am thankful to my sister and brother for the ir love and support. Lastly, t o my parents, for all their efforts , sacrifices and patience , to provide us with everything for a better future. Without their love , understanding and prayers it would have been impossible for me t o complete my research . vi TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ............................. viii LIST OF FIGURES ................................ ................................ ............................... x 1 Introduction ................................ ................................ ................................ .... 1 1.1 Motivation ................................ ................................ ................................ 1 1.2 Background ................................ ................................ ............................. 1 1.2.1 P ositron Emission Tomography ................................ ........................... 1 1.2.2 Computed Tomography ................................ ................................ ....... 5 1.2.3 Hybrid Single Gantry PET/CT System ................................ ................. 9 1.3 Research Problem ................................ ................................ ................ 11 1.4 Approac hes to Eliminate PET/CT Artifacts ................................ ............ 14 1.5 Challenges ................................ ................................ ............................ 16 2 A ttenuation Correction in PET B rain Data ................................ ................. 18 2.1 Introduction ................................ ................................ ........................... 18 2.2 Data Acqui sition ................................ ................................ .................... 20 2.3 Brain Segmentation ................................ ................................ ............... 20 2.3.1 Segmentation of CT Brain Images ................................ ..................... 21 2.3.2 Segmentation of PET Brain Images ................................ ................... 24 2.4 PET/CT Brain Registration ................................ ................................ .... 26 2.4.1 Preprocessing ................................ ................................ .................... 26 2.4.2 Translational Registration ................................ ................................ .. 26 2.4.3 Rotational Registration ................................ ................................ ....... 28 2.4.4 Image Registration Res ults ................................ ................................ 29 2.5 PET Reconstruction ................................ ................................ .............. 32 3 Attenuation Correction of Cardiac Data ................................ ..................... 42 3.1 Data Acquisition ................................ ................................ .................... 43 3.2 Cardiac Image Segmentation ................................ ................................ 43 3.2.1 Fuzzy Clustering ................................ ................................ ................ 48 3.2.2 Masking ................................ ................................ ............................. 48 3.2.3 Edge Detection ................................ ................................ .................. 50 3.3 PET/CT Image Registration ................................ ................................ .. 55 3.3.1 Image Registration Results ................................ ................................ 57 3.3.2 Analysis of PET/CT Image Registration ................................ ............. 59 3.4 PET Reconstruction ................................ ................................ .............. 63 3.5 Polar map Representation of PET Cardiac Data ................................ ... 67 4 Optimal Respiratory and Cardiac Phases ................................ .................. 71 4.1 Introduction ................................ ................................ ........................... 71 4.2 Evaluation of Multiple Respiratory Phase s ................................ ............ 72 4.2.1 Data Acquisition ................................ ................................ ................. 72 vii 4.2.2 PET/CT Image Registration Results ................................ .................. 73 4.2.3 PET Image Reconstruction Results ................................ ................... 77 4.3 Validation of the Optimal Cardiac Phase ................................ ............... 81 4.3.1 Data Acquisition ................................ ................................ ................. 81 4.3.2 Maximizing the PET/CT Cardiac Overlap ................................ .......... 82 4.3.3 Methodology ................................ ................................ ...................... 83 4.3.4 Results ................................ ................................ ............................... 86 4.3.5 Analysis of Un gated and End - D iastolic CTAC s ................................ . 90 4.3.6 PET Image Reconstruction ................................ ................................ 91 5 M anual vs . Automated Registration ................................ ........................... 93 5.1 Introduction ................................ ................................ ........................... 93 5.2 Data Acquisition ................................ ................................ .................... 94 5.3 Manual Registration Process ................................ ................................ 94 5.3.1 Quantitative Analysis of the Shift Values ................................ ........... 99 5.3.2 User - Dependent Shift Variations ................................ ...................... 101 5.3.3 Co mparison of Unshifted and S hifted Image Reconstruction s ......... 102 5.4 Automated vs. Manual Registration ................................ .................... 103 6 Discussion ................................ ................................ ................................ .. 110 6.1 Effects of Overc orrection ................................ ................................ ..... 112 6.2 Heart and Lung Volume Correlation ................................ .................... 116 6.3 Attenuation - Corrected and Non Attenuation - Corrected Data .............. 118 6.4 Hyper - perfusion Artifact ................................ ................................ ...... 119 7 Summa ry and Future Work ................................ ................................ ....... 121 7.1 Summary ................................ ................................ ............................. 121 7.2 Contributions ................................ ................................ ....................... 123 7.3 Future Work ................................ ................................ ........................ 124 7.3.1 Dual Gating for PET Data Acquisition ................................ .............. 124 7.3.2 Left Ventricle Deformation Correction ................................ .............. 125 7.3.3 Estimation of Myocardial Blood Perfusion ................................ ........ 126 7.4 Papers Written ................................ ................................ .................... 129 BIBLIOGRAPHY ................................ ................................ .............................. 130 viii LIST OF TABLES 2 1 Table 3.1: Image acquisition parameters for PET/C T imaging system of cardiac 30 44 Table 3.2: Shifts in the x, y, and z directions required to compensate for the misregistration between the PET and CT images in fifty patients .......................... 6 1 Table 4.1: Means and standard deviations of the shift values required in the sagittal plane for multiple CTACs acquired at different respiratory phases 74 Table 4.2: Average shift values required for ungated CTAC and the ECG gated end - diastolic ...... 91 94 Table 5.2: Average shift values for the manual alignment 100 Table 5.3: Average shift values required in each pl ane 100 Table 5.4: Shift values obtained using our automated software applied to the PET/CT data collected during the rest exam 105 Table 5.5: Shift values obtained using our automated software applied to the PET/CT data collected during the stress exam 105 Table 5.6: Average shift values obtained from four users using manual alignment applied to the PET/CT data collected during the rest exam .. 106 Table 5.7: Average shif t values obtained from four users using manual alignment applied to the PET/CT data collected during the stress exam 106 Table 5.8: Maximum shift values obtained from four users using manual alignment applied to the PET/CT data collected d uring the rest exam .. .................................... 107 Table 5.9: Maximum shift values obtained from four users using manual alignment applied to the PET/CT data collected during the stress exam . ................................. 107 Tabl e 5.10: Difference in the shift values between the automatically registered and the average manual shifts in the rest exams ............ .......... .................... 108 ix Table 5.11: Difference in the shift values between the automatically regist ered and the average manual shifts in the stress exams ............................ 108 Table 5.12: Difference in the shift values between the automatically registered and the maximum manual shifts in the rest exams .................. ............ 109 Table 5.13: Difference in the shift values between the automatically registered and the maximum manual shifts in the stress exams .......................... 109 x LI ST OF FIGURES Figure 1.1: The process of positron emission tomography imaging. (a) The proton - rich radioactive nucleus, (b) decay of the unstable nucleus resulting in the emission of a positron, (c) annihilation of the positron and the electron, and (d) t he annihilation resulting in two anti - 3 Figure 1.2: The process of detecting true coincidences with pairing signals at 3 Figure 1.3: S 4 Figure 1.4: Multiple x - ray projections are collected at different angles to acquire a cross - 6 Figure 1.5: (a) Shows the proces s of capturing projections of an object from various angles (b) shows the projection profile from position A, (c) shows the projection profile from position B, (d) shows the projection profile from position C, (e) shoes the projection profile from position D, and (f) shows the reconstruction of the object 7 Figure 1.6: Helical CT scanning, where z represents the distance covered in 8 10 10 13 Fi gure 1.10: PET reconstruction using (a) misaligned PET and CT images, and (b) 14 Figure 2.1: The segmentation results for the CT images, where (a) shows a set of unpr ocessed CT slices in the axial plane, and (b) shows the same CT slices after 23 Figure 2.2: The segmentation results for the PET images, where (a) shows the unprocessed PET slices in the axial plane, and (b) shows the same PET slices after the images are segmented. The selected axial slices are evenly distributed within the 47 slice dataset. Even with significant differences in the shape of the brain structure among these slices, t he segmentation process performs well in 25 xi Figure 2.3: PET/CT image registration results, where the white lines represent the PET brain contours and the gray scale images show the CT brain. Fig. 3 (a - c ) illustrates the original PET and CT data for slice number 33 in the axial plane, slice 64 in the sagittal plane, and slice 64 in the coronal plane, respectively. Fig. 3 (d - f) shows the results of translational registration in the axial, sagittal and coro nal planes. Fig. 3 (g - i) demonstrates a significant improvement after translational and rotational registration 32 Figure 2.4: Reconstructed PET images using misaligned and aligned CTACs. Fig. 2.4 (a - c) shows the rec onstructed PET slices in the axial, sagittal, and the coronal planes using the misaligned CTAC. Fig. 2.4 (d - f) shows the same reconstructed PET slices in the axial, sagittal, and coronal planes using the aligned CTAC .. 34 Figure 2.5: PET image rec onstruction using misaligned and aligned CTACs for patient number 6. Fig. 2.5 (a) shows sagittal slice number 64 of the misaligned PET and CT images, Fig. 2.5(b) shows the same sagittal slice after the PET and CT images are registered, Fig. 2.5(c) shows th e reconstructed PET image using the misaligned CT image, and Fig. 2.5(d) shows the sagittal PET slice reconstructed using the aligned CTAC 36 Figure 2.6: Reconstructed PET images using misaligned and aligned CTACs for patient number 8. Fig. 2.6 (a) shows axial slice number 24 of the misaligned PET and CT images, Fig. 2.6(b) shows the same slice after the PET and CT images are registered, Fig. 2.6(c) shows the reconstructed PET image using the misaligned CTAC, and Fig. 2 .6(d) shows the axial PET slice reconstructed using the aligned CTAC 39 Figure 2.7: Reconstructed PET images using misaligned and aligned CTACs for patient number 8. Fig. 2.7 (a) shows axial slice number 33 of the misaligned PET and CT images, Fig. 2.7(b) shows the same slice after the PET and CT images are registered, Fig. 2.7(c) shows the reconstructed PET image with the misaligned CTAC using the jet colormap in Matlab, and Fig. 2.7(d) shows the axial PET slice re constructed with the aligned CTAC using the jet colormap in Matlab 40 Figure 2.8: Reconstructed PET images using misaligned and aligned CTACs for patient number 10. Fig. 2.8 (a) shows coronal slice number 64 of the misaligned PET and CT images, Fig. 2.8(b) shows the same coronal slice after the PET and CT images are registered, Fig. 2.8(c) shows the reconstructed PET image using the misaligned CTAC, and Fig. 2.8(d) shows the sagittal PET slice reconstructed using the aligned CTAC 41 Figure 3.1: Averaging results in the axial plane, where (a) shows the unweighted 46 Figure 3.2: Averaging in the axial plane indicates which slices to process in the sagittal direction 46 xii Figure 3.3: Averaging results in the coronal plane, where (a) shows the unweighted 47 Figure 3.4: Averaging in the coronal plane indicates which slices to process in the axial direction 47 Figure 3.5: Results of the pre - processing steps in the axial plane, where (a) shows unprocessed axial slice number 23, (b) shows the image after fuz zy clustering is applied, (c) shows the binary mask, and (d) shows the extracted 49 Figure 3.6: Result obtained after masking in the sagittal plane, where (a) shows the 50 Figure 3.7: Results of the pre - processing steps applied to the PET image, where (a) shows the original axial image, slice number 40 (z - axis coordinate 102.39 mm), (b) shows the fuzzy clustered image containing the cardiac cluster and the unwant ed liver cluster, (c) shows the masked image in which the liver cluster is removed, and (d) shows the extracted contour of the cardiac region .. 53 Figure 3.8: Result of the processed images in the sagittal plane, where (a) shows the original PET image, (b) shows the contour obtained from the processed PET image, (c) shows the original CT image, and (d) shows the contour obtained from the low - pass filtered CT image 54 Figure 3.9: Axial plane slice 24, (a) misregis tered image, and (b) after the cardiac geometries are aligned with the automated registration procedure 58 Figure 3.10: Axial Plane slice 33, (a) misregistered image, and (b) after the cardiac geometries are aligned with the automated reg istration procedure 58 Figure 3.11: PET/CT registration results in the sagittal plane, where the top half portions of (a) and (b) are misaligned, and the lower half portions show the aligned images 59 Figure 3.12: Distribution of the shift values due to the misregistration between PET and CT images (a) in the x direction, (b) in the y direction, and (c) in the z direction.... 62 Figure 3.13: Axial CT slice 24 of patient 1 from Table 2 with an ov erlaid PET heart contour, where (a) shows misregistered PET and CT images; (b) shows the result after the cardiac geometries are automatically aligned by the registration software; (c) shows the PET image reconstructed using the misaligned CT image; and (d ) shows the same PET image reconstructed using the aligned CT image .. 64 Figure 3.14: PET images reconstructed with a misaligned CTAC demonstrate artifactual hypoperfusion 66 xiii Figure 3.15: The same PET data used in Fig 3.14, reconstructed using the aligned CTAC, indicate normal perfusion 66 Figure 3.16: A polar map is created from the short axis slices of the heart 69 Figure 3.17: PET images in the axial plane recons tructed using (a) misaligned CT data and (b) aligned CT data. PET images in the coronal plane reconstructed using (c) misaligned CT data and (d) aligned CT data 70 Figure 3.18: Polar maps of reconstructed PET data using (a) misalig ned CT data, and (b) aligned CT data 70 Figure 4.1: Contours of PET cardiac images superimposed onto the four CTACs evaluated in the sagittal plane, slice number 78 (y=63.5 mm), before alignment. The results before re gistration are shown for (a) end normal expiration acquired before the PET stress exam (CTAC1), (b) end normal expiration acquired after the PET stress exam (CTAC2), (c) halfway through normal end expiration (CTAC3), and (d) forced end expiration (CTAC4) . .. 75 Figure 4.2: Contours of PET cardiac images superimposed onto the four CTACs evaluated in the sagittal plane, slice number 78 (y=63.5 mm), after alignment. The results after registration are shown for (e) end normal ex piration acquired before the PET stress exam (CTAC1), (f) end normal expiration acquired after the PET stress exam (CTAC2), (g) halfway through normal end expiration (CTAC3), and (h) forced end expiration (CTAC4) 76 Figure 4 .3: Sagittal slice 78 (y=63.5 mm) of the PET data reconstructed using unregistered CTACs. Results of PET reconstruction are shown for (a) unregistered CTAC1, (b) unregistered CTAC2, (c) unregistered CTAC3, and (d) unregistered CTAC4 79 Figure 4.4: Sagittal slice 78 (y=63.5 mm) of the PET data reconstructed using registered CTACs. The reconstructed PET results are shown for (a) registered CTAC1, (b) registered CTAC2, (c) registered CTAC3, and (d) registered CTAC4. Fig . 4.4 (a - d) indicates that the perfusion is normal in the entire cardiac region and that the hypoperfusion was an artifact produced by the unregistered CT images 80 Figure 4.5: CT attenuation map generated by averaging all of the CT datasets obta ined at different cardiac phases 84 Figure 4.6: CT attenuation map generated by taking the maximum value of each pixel from all of the CT datasets obtained at different cardiac phases 85 Figure 4.7: Contours of th e PET image overlaid onto the corresponding CT image at different cardiac phases: (a) the 70% cardiac phase, which corresponds to diastole, and (b) the 30% cardiac phase, which corresponds to systole 88 xiv Figure 4.8: PET cardiac contours in the sagittal plane registered with the corresponding CT images acquired during (a) the diastolic phase and (b) the systolic phase 89 Figure 4.9: Sagittal PET slice reconstructed using (a) a diastolic phase CTAC and (b) a systolic phase CTAC 92 Figure 5.1: Left ventricle activity in the PET image misaligned with the lung in the CT image. Many lines of response (LOR) for the left ventricle activity do not pass through cardiac tissue i n the CTAC. PET image reconstruction performs the attenuation correction as if photons originating from left wall of the left ventricle passed through only lung/air 97 Figure 5.2: Reconstructed PET images using a misaligned CTAC, along (a) the long axis, (b) the short axis, and (c) the corresponding polar map 97 Figure 5.3: Left ventricle activity in the PET image that is manually aligned with the cardiac region in the CT image r esulting in accurate attenuation correction in the left ventricle. In this image, since the lines of response originating in the cardiac region in the PET data pass through the corresponding cardiac region in the CT data, the correct attenuation parameters are assigned during the reconstruction of the PET data ........ 98 Figure 5.4: Reconstructed PET images using a manually aligned CTAC, along (a) the long axis, (b) the short axis, and (c) the corresponding polar map ...... 98 Figure 5.5: Difference in the shift values in the axial plane for the same patient by two users ..................................................................................... ............ 102 Figure 5.6: Difference i n the shift values in the coronal plane for the same patient by two users ....... 102 Figure 6.1: PET cardiac region overlaid onto (a) the misaligned CTAC in the axial plane, (b) the misaligned CTAC in the coronal plane, (c) the aligned CTAC in the axial plane, and (d) the aligned CTAC in the coronal plane ... 114 Figure 6.2: Polar plot of the reconstructed PET data generated using the (a) m isaligned CTAC and (b) the aligned CTAC. The comparison shows that attenuation artifacts were present in the PET data reconstructed using the misaligned CTAC 115 Figure 6.3: Polar plot of the difference between the PET data reconstructed using the misaligned CTAC and the aligned CTAC shows that even though there was a significant misalignment between the PET and CT data, the error in the xv reconstructed PET data is much smaller than the errors caused when the PET heart ov erlaps with the lung in the CT image ....... ............................................................... 115 Figure 6.4: Normalized volumes of the heart and lung within different cardiac phases using the values calculated from segmented CT data 117 Figure 6.5: Contours of the heart in the 30% cardiac phase, which corresponds to systole, and the 70% cardiac phase, which corresponds to diastole. The systolic cardiac volume shown in blue is significantly smaller than the diastolic cardiac volume shown in green 118 Figure 6.6: Calcification in the heart (a) is observed in the CT slice in the axial plane, and (b) causes a hyperperfusion artifact in the reconstructed PET slice ... 120 Fi gure 7.1: Transformation of the left ventricle during the cardiac beat cycle where (a) shows two point on the myocardial wall, and (b) shows that the same points do not overlap when the cardiac wall is warped 126 Figure 7.2: G raphical interface for viewing cardiac PET data and for generating and analyzing the polar maps 127 Figure 7.3: Polar maps of the cardiac data acquired at different times 128 1 1 Introduction 1.1 Motivation PET/CT is a rapidly growing , non - invasive technology for diagnosing different types of functional abnormalities of various organs. Although PET/CT has shown promising results , the misregistration between PET data and CT attenuation map s often produces arti factual abnormalities in the PET images re sulting in false positive s [ 1 - 8 ] . A whole - body PET scan takes between 15 - 30 minutes, and patient movement is inevitable during the PET data acquisition [9]. The patient motions that occur can be classified as volun tary mot ions or involuntary motions. [9 - 11]. Voluntary motions are described as the physical movement of the patient during a PET scan , which can be due to discomfort or pain, whereas involuntary movement is due to the transformation of the heart and lungs during cardiac and respiratory cycles [12 ] . Unlike PET imaging , which acqu ires data continuously during the scan, CT imaging collects an instantaneous snapshot of the anatomy at a specific point in the respiratory or cardiac cycle. Due to the sequential a cquisition of CT and PET data, both voluntar y and involuntary movements affect the alignment of the organs in the two modalit ies. Therefore, CT images are frequently misaligned with the longer duration PET scans [ 5 ]. 1.2 Background 1.2.1 Positron Emission Tomograph y Positron E mission Tomography (PET) shows the functional organ information using radionuclide tracer s to track metabolic activity or perfusion rate based on the type of the radiopharmaceutical [13 - 14] . For PET imaging with fludeoxyglucose (FDG), the PET 2 i mage shows the metabolism in terms of the regional glucose uptake [ 14 ]. Although FDG is the most common PET tracer, other tracers can also be used in PET imaging [ 14 ]. The PET scanning process consists of coincidence detection, attenuation correction , and image reconstruction as described in the following sections. Radioactive Tracer Injection As the first step of PET data acquisition, a radionuclide tracer with a relatively short half - life is administered in the body. Once the tracer starts to decay, posit ively charged particle s , namely positron s , are emitted. The se positron s collide with electron s in the body , resulting in the annihilation of both particles and producing a pair of 511 keV gamma photons moving in opposite directions. The complete process is depicted in Fig. 1.1 , which shows the stages of radioactive decay followed by the positron - electron anni hilation, resulting in a pair of anti - parallel gamma rays. Th ese high energy photons are dete cted by a ring of detectors around the body [ 15 - 16 ]. Coin cidence Detection On c e the gamma rays are detected , coincidences are estimated using a short time window. Within this window, if tw o gamma rays are detected at opposite detectors, then the point o f annihilation is calculated on the line of response (LOR) j oining the two detectors. The location of the annihilation on the specific line of response is calculated using the time difference in the detection of the pair of gamma rays. Fig. 1.2 shows the process of selecting only coincidence - detected gamma rays wit hin a given time window. 3 Figure 1.1 : The process of positron emission tomography imaging. (a) The proton - rich radioactive nucleus, (b) decay of the unstable nucleus resulting in the emission of a positron, (c) annihilation of the positron and the electro n, and (d) the annihilation resulting in two anti - parallel gamma rays. Figure 1.2 : The process of detecting true coincidences with pairing signals at opposite detectors within a specified time window. 4 Reconstructed PET Images Using the coincidence - det ected data, PET image s are reconstructed as shown in Fig. 1.3. The figure shows a set of selected images in the axial plane from a cardiac exam of a patient. These images show the liver as well as the left ventricle of the heart which is due to the high am ount of tracer uptake in these organs. Figure 1.3 : Selected set of cardiac PET images in the axial plane. 5 Attenuation Correction Depending on the anatomical structures that the gamma rays pass through before hitting the detector, the attenuation of t hese rays can vary significantly . If the attenuation factor is not taken into account at the time of image reconstruction , the n the anatomical structures deep in the body can appear to have much low er tracer uptake [17 - 19] . To avoid this, PET /CT imaging sy stems have an integrated CT scanner to acquire the CT data that is used as the anatomical attenuation map for the PET reconstruction [20] . Although CT based atten uation maps generally provide good PET reconstruction, CT based attenuation can sometimes indu ce significant artifacts due to patient motion [21] . To avoid this problem , the PET and CT datasets are examined for any artifact s prior to the reconstruction process . 1.2.2 Computed Tomography In CT imaging , multiple X - ray projections are acquired at differen t angles around the object as shown in Fig. 1.4 . These projection s , along with the atten uation coefficients of various anatomical structure s , are used to reconstruct the cross - sectional image with filtered back - projection [22 - 30 ] as shown in Fig. 1.5 . Mult iple cross - sectional scans are acquired with a slight shift in the axial position of the body in order to create three dimensional volumetric data that describes the anatomical structures. 6 Figure 1.4 : Multiple x - ray projections are collected at different angles to acquire a cross - sectional CT image of the object . 7 (a) (f) (b) (c) (d) (e) Figure 1.5 : (a) Shows the process of capturing projections of an object from various angles (b ) shows the proje ction profile from position A, (c) shows the projection profile from position B, (d) shows the projection profile from position C, (e) shoes the projection profile from position D, and (f) shows the reconstruction of the object using these four projections . The CT attenuation for homoge nous and inhomogeneous (heterogeneous) media is given by [26] (1.1) and , (1.2) 8 respectively. In Eqs. 1.1 and 1.2, is the projected attenuation , is the i ntensity of the incident x - ray , is th e intensity after attenuation through the object, and is the attenuation c oeffi cient that varies as a function of space. The CT data is acquired using axial or helical scanni ng. In axial scanning, the bed position is adjusted in steps and each slice is acquired . I n helical scanning , as shown in Fig . 1.6 , the bed slides at a fixed speed while the scanner continuously acquires a series of projection s [31 ]. Relative to axial scanning , helica l scann ing reduces the time to adjust the bed for each slice. Also , since helical scanning provides continuous projections, the image s can be reconstructed using different slice thickness value s as desired. Fig. 1.6 shows an example of single detector heli cal CT scanner. In modern scanners, multip le detector rings are used to scan a wider area in one rotation [32 - 33 ] . Figure 1.6: H elical CT scanning , where distance covered is represented in millimeters, and the time elapsed is represented in seconds. 9 T he reconstructed image from a CT scan is a two dimensional array of pixel s in which each pixel corresponds to a specific location in the body. The value of each pixel is calculated in terms of Hounsfield units using [26] . (1.3) The CT number is calculated using the attenuation coefficients of different anatomical pixel water ) . For v alues of pixel that are water , the r esult ing CT number is negative , where - 1000 corresp onds to air. For v pixel water , the CT number is positive , which correspond s to other soft tissues and bone. A set of reconstructed CT images from a brain scan of a patient are shown in the axial plane in Fig. 1.7 . 1.2.3 Hybrid Single Gant ry PET/CT System Hybrid PET /CT systems [34 - 35] combine two modalities in a single unit, thus providing functional and anatomical data in a single setup. Fig. 1.8 shows the schematic of the original PET/CT prototype developed by Beyer et al [63] . The othe r advantage of the hybrid approach is that CT images , which only take a few seconds to acquire , provide excellent resolution for the attenuation map in PET image reconstruction [ 36 ] . 10 Figure 1.7: Selected set of brain CT images in the axial plane. Fig ure 1.8 : Representation of a PET/CT scanner . 11 A t the beginning of a PET scan , the tracer is administered to the patient . After a waiting period of around one hour, the patient is positioned on the bed of the scanner for CT data acquisition. Once the CT sc an is completed, the bed position is adj usted to start the PET scanning. The purpose of acquiring the CT images is to perform the attenuation correction of the PET data before the reconstruction process [37]. The main advantage of PET/CT is the shorter ove rall acquisition time , which results in greater patient throughput. In a traditional standalone PET system, the time required to obtain the transmission map is about 30 - 40% of the total scan time, which is on the order of several minutes [39 - 40 ] . In contra st, CT scans for attenuation correction are acquired in a few seconds. Another advantage of CT based attenuation correction is the lower noise level in CT images compared to traditional transmission scans, resulting in reconstructe d PET images with higher signal - to - noise ratios. Also, PET/CT improves the localization of abnormal tracer uptake in small regions which may be difficult to identify in standalone PET scans. 1.3 Research Problem In hybrid PET - CT imaging, patient motion (voluntary or involun tary) is a major concern in clinical applica tion s , where motion during PET data acquisition results in erroneous position s calculated for the detected photon s [41] . The imaging process consists of a CT scan followed by a PET scan, and the patients are i nstructed to k eep still for the entire duration so that the CT and PET images are properly aligned. A lignment is important for both accurate spatial localization of tracer activity and accurate attenuation correction. Certain steps are taken in order to minimize the p a tient motion , such as: (a) verbal 12 instructions to the patient to stay still ; (b) making sure that the patient is in a comfortable position before the data acquisition starts ; (c) having patients empty their bladder before the start of the study; an d (d) us ing head holders and restraining tape for brain imaging [42 ,56 ] . Despite t hese precautionary measures, respiratory and cardiac motion is nevertheless unavoidable . A comm on problem is demonstrated in Fig. 1.9 , which shows the PET cardiac contour overlaid on to the CT image. Because of the misali gnment between the CT and PET data, the cardiac region in the PET image is projected onto the lung in the CT image . The white lines represent two different lines of response for the gamma rays generated by positron - ele ctron annihilation event s. These lines pass through the soft tissue of the myocardium , but due to the misaligned CT images , they appear to be travelling through the lung. When PET images are reconstructed using this misaligned CT attenuation correction (CT AC) map, erroneous values of the attenuation parameter associated with air (from the lung) are assigned to pixels along these lines, resulting in a n under - compensated region showing a significant hypoperfusion artifact. 13 Figure 1.9 : Misma tch between the PET and CT images in a cardiac study . The PET images for this study are reconstructed first using the misaligned CTAC and then using an aligned CTAC. The results of the se two reconstructed P ET images are shown in Fig. 1.10. The first image, Fig. 1.10 (a) , shows artifactual hypoperfusion in the anterolateral wall, whereas the second image, Fig. 1. 10 (b) shows uniform pe rfusion throughout. Fig. 1.10 (a) depict s the problem caused by a misaligned CTAC in PET/CT imaging , which if un corrected, may require the patient to go through an unnecessary invasive procedure. 14 (a) (b) Figure 1.10 : PET reconstruction using (a) misaligned PET and CT images, and (b) reconstruction after the PET and CT datasets are aligned. [[ 1.4 Approaches to Eliminate PET/CT Artifacts One approach to address the PET/CT misalignment problem is to obtain multiple CT scans during different respiratory phases in a cardiac exam. The PET images are matched with the CT images, and the CT scan with the smallest registration error is selected for P ET attenuation correction [ 43 - 44 ] . This method does not guarantee consistent align ment of PET and CT images because respiratory motion varies between 15 the PET and the CT exam s , particularly when the patient is imaged under a PET stress condition, which can alter the respiratory rate an d excursion. In some cases, all of the CT scans are mis ali gned with the PET data, which introduces hypoperfusion artifacts into all of the reconstructed PET images. The inconsistent alignment between the PET and CT images denie s the possibility of using one unregistered respiratory phase for attenuation correction, which reinforces the need for multiple CT scans if no registration software is available . If multiple CT scans are acquired, then the patient is exposed to an unneces sary radiation dose that can be avoided if software - aligned PET and CT images are used . Each CT scan delivers a CT dose index volume (CTDIvol) of 2.35 mGy to the patient, and by acquiring four CT scans, a total CTDIvol of 9.4 mGy is delivered to the patien t. The dose length product (DLP) for a single CT scan is 43.10 mGy - cm, and for four CTACs, the total DLP is 172.4 mGy - cm [45 - 46 ] . With growing concerns over the radiological risks of CT, radiation dose reduction is very important, and by acquiring only one CTAC for every patient instead of four, a significant reduction in the radiation dose is achieved [47 - 49 ] . Also, the multiple CT acquisition approach is also in efficient in terms of the clinical workflow. If multiple CTACs are acquired for every patient, then each CTAC is loaded onto the console and superimposed onto the PET images. If the first CTAC does not align properly with the PET image, then the next CTAC is loaded and compared with the PET image. This process, which is repeated for each CTAC, is po tentially time - consuming and is otherwise inefficient in terms of clinical resources. Another possible ap proach reduce s the temporal resolution of the CT to match that of the PET examination. This is achieved with an ultra slow CT acquisition or a respirati on - averaged CT. These approaches can reduce the breathing - induced misalignment at the 16 expense of increased radiation dose for the patient or longer acquisition times. However, misalignment resulting from other sources, such as patient motion or changes of the heart location due to pharmacologic stress agents remains uncorrected with this approach. Manual regis tration is another option, but this adds the inconvenience of being time - consuming and observer - dependent. A better solution to this problem is provid ed by a software program that automatically registers the two modalities and eliminates the attenuation artifacts from the reconstructed PET. The software - based method introduced here aligns the PET and CT data by calculating the distance between the bound arie s of the PET and CT brain or heart. An aligned CT attenuation correction (CTAC) map is generated using the shift values obtained from PET/CT imag e registration. The PET data is then reconstructed using the shifted CT images , which yields a much better result. This approach also eliminates the need for multiple CTACs, t hus reducing the radiation dose for the patient . Also, relative to manual registration, automated PET/CT image registration is much more time efficient , which improves the overall clinical workflow. The registration process is also independent of the respiratory phase of CT in cardiac studies , where the new automated approach consistently produces effective registration results for all respiratory phases . 1.5 Challenges The following challeng es need to be addressed to improve PET/CT registration in a clinical environment: 1. The algorithms developed for aligning the CTAC with the PET data need to be efficient in order to improve the clinical workflow relative to manual registration. 17 The complete process , including reading and generating aligned images , should not take more than a few minutes. 2. All of the results obtained from the training datasets need to be validated by an expert through comparisons with manual registration results . Th is analysis is required to ensure the accuracy of the system. 3. The Digital Imaging and Communications in Medicine (DICOM) images gener ated by the software must be compatible with th e GE Discovery STE scanner. N ew unique identifiers (UIDs) are also required so that no o ther imaging study has the same UID. 18 2 Attenuation Correction in PET Brain Data 1 2.1 Introduction In most neurological applications, the ability of positron emission tomography (PET) to measure metabolic activity has significant implications in diagnosing Alz heimer's disease, frontotemporal dementia, epilepsy, and other neurological conditions because of the relative changes in the glucose metabolism associated with specific disease conditions [50 - 53] . Such abnormal metabolic activity regions are accurately lo calized within specific areas of the brain with the help of the anatomical detail provided by the computed tomography (CT) scan [54] . To minimize problems with misregistration artifacts, patients are instructed to remain still during the acquisition proces s. In most cases, this is a difficult task because a significant percentage of the patients who are required to have a PET/CT exam are demented and cannot follow the verbal instructions given b y the technologist. T hese patients are often imaged using a he ad - holder device with restraining tape across their foreheads [55 - 56] . Despite these immobilization techniques , many patients still tend to move throughout the image acquisition process, resulting in highly misaligned PET and CT images. In such cases, the CT scan is repeated in order to obtain a set of images that align with the PET data. _____________________________________________________ 1 Reproduced from K. Khurshid, K. L. Berger, R. J. McGough, Automated PET/CT Brain Registration for Accurate Attenu ation Correction, Engineering in Me dicine and Biology Society , USA, 2009, with the permission of IEEE. 19 The major drawbacks of this approach are that acquiring multiple CT scans increases the radiati on dose for the patient and that there is no guarantee th e second CT will be aligned. These problems can be avoided if automated software registration techniques are used. To improve PET reconstruction using a CT attenuation correction (CT AC) map, automated software has been developed to automatically align the two modalities and generate an attenuation map that is registered with the PET images . has been developed. This software eliminates the need for acquiring multiple CTACs and therefore improves the overall clinical workflow. The software - aligned CTAC is the n used for the reconstruction of the PET images . This procedure has been tested on PET/CT data acquired from ten patients. Among the ten patients, fou r showed significant misregistration error s between the PET and CT brain geometries. The other six dataset s were aligned correctly or contained a very small misregistration error that had little or no effect on the reconstruction of the PET images . For all ten patients, the software successfully segmented the brain in the PET and CT images and correctly aligne d the segmented brain structures obtained from the two modalities. Based on the translational and rotational motion compensation that is applied to the CT images , an aligned CTAC is generated. The reconstruction of PET data is carried out using the new CTA C, and the results show that the attenuation artifact due to the PET/CT misregistration , when present, is eliminated from the reconstructed PET images . For the datasets with no inherent misregistration error, the PET images were reconstructed with the orig inal CTAC s, and the results were the same. 20 2.2 Data Acquisition A study was performed with prior consent from ten patients. The imaging procedure included a standard PET and CT scan protocol that was approved by the internal review board (IRB) at Michigan Sta te University . PET/CT scans were acquired for ten consecutive patients , an d no prior history was taken into consideration . The scans were acquired using the GE Discovery STE fusion PET/CT scanner , which combines a helical 16 row CT scanner and a full ring PET tomograph with a Bismuth Germanate (BGO) block for detecting high energy photons [57] . H elical CT scans of the head were acquired covering 15.4 cm along the z - ax is with a 0.8 sec rotation speed , 11.75 mm per rotation table speed, 140 kVp tube voltage, and 65mA tube current . The CT images were re constructed in 47 axial slices with 512x512 pixels, 3.75 mm slice th ickness, 0.97 mm pixel spacing, and 16 bits per pixel . The PET scan also covered 15.4 cm along the z - axis with a crystal size of 4.7 mm x 6.3mm x 30 mm. The reconstructed P ET data consisted of 47 slices with 128x128 pixels, 3.27 mm slice thickness, 2.34 mm pixel spacing, and 16 bits per pixel . The parameters for the CT and PET images are listed in Table 2.1. 2.3 Brain Segmentation Before the two moda lities are aligned, the PET and CT images are segmented in order to extract the brain region . The details of the segmentation process are provided in the following sections. 21 Table 2.1: CT and PET imaging parameters for the brain studies. CT Width 512 pixe ls Height 512 pixels Bit Depth 16 bits Color Type Grayscale Slice Thickness 3.75mm Field of View 500mm x 500mm Pixel Spacing 0.9766mm Table Speed 14.0625mm/s Revolution Time 0.8s Table Feed Per Rotation 11.25mm Spiral Pitch Factor 0.562 5 PET Width 128 pixels Height 128 pixels Bit Depth 16 bits Color Type Grayscale Slice Thickness 3.27mm Field of View 300mm x 300mm Pixel Spacing 2.3438mm Radioactive Tracer Fluorodeoxyglucose (FDG) 2.3.1 Segmentation of CT Brain Images The CT im ages are first processed with a low pass filter to smooth the boundary of the brain and to reduce the image noise. To segment the brain from the CT data, a seed based reg ion - growing technique is used [58 - 59] . The seed point is selected by calculating the m ean of the pixel coordinates with Hounsfield unit s (HU) equal to 40 , which 22 corresponds to brain matter [60] . Selecting a value equal to 40 instead of a range of values reduces the total number of coordinates resulting in faster processing. By averaging the se selected coordinates , an approximate center point of the brain is estimated. This seed point or the estimated center of the brain is used as the starting location for the segmentation process. The single - seed region growing technique i s fast and easy to implement. First , the seed point is marked as the current pixel and the pixel value is set to 1. Then , all 26 of the connected neighboring pixels are identified from the 3D CT data. The neighboring pixels with Hounsfield unit s corresponding to the brain a re pushed into a processing queue . T he remaining neighboring pixels are set to zero , and the first iteration is completed. For the second iteration , the pixel at the top of the queue is popped , and the same process of selecting the neighbors is repeated. I n the second iteration , only those neighboring pixels which are not already present in the queue are pushed into the queue. All of the pixels are popped one by one from the top of the queue , and the new selected neighbors are added to the queue. This proce ss is repeated until the queue is empty, which means all of the connected pixels corresponding to the brain matter are marked with 1 and the remaining pixels are set to zero. This process segments the brain in 3D such that all of the anatomical structures that are not connected to the brain are automatically r emoved. The total number of pixels with a value of 1 gives the total volume of the brain , which is used as an additional boundary condition while segmenting the PET brain. This process, which is simila r to watershed segmentation [61] , yields the same segmentation results in less time. Fig. 2 .1 (a) - (b) shows the CT segmentation results for a representative patient. Fig. 2 .1 (a) shows ten unprocessed CT slices ( slice number 6, 10, 14, 18, 22, 26, 30, 34 , 38, and 23 42) in the axia l plane out of 47 slices. Fig. 2 .1 (b) shows the same axial slices after the segmentation has been performed and all of the unwanted structures are removed. Only the b rain remains in Fig. 2 .1 (b), and these results are subsequently used for image registration. (a) Unprocessed CT slice numbers 6, 10, 14, 18, 22, 26, 30, 34, 38, and 42. (b) Segmented CT slice numbers 6, 10, 14, 18, 22, 26, 30, 34, 38, and 42. Figure 2 .1 : The segmentation results for the CT images, where (a) sho ws a set of unprocessed CT slices in the axial plane, and (b) shows the same CT slices after s egmentation . 24 2.3.2 Segmentation of P ET Brain Images The brain in the PET images is segmented using the same region - growing approach used for the CT images . The seed po int is calculated by averaging the coordinates of the segmented C T brain , which gives an estimate for the center of the brain region. Star ting from this location, the 26 connect ed neighboring pixels are set to either 0 or 1 based on the intensity of these pixels. All of the neighboring pixels with intensity value s greater than 50 are set to 1, as these pixels represent the presence of metabolic activity. The rest of the neighboring pixels are set to 0. The same process is then repeated for one of the neighb oring pixel s that was set to 1 in the previous step. The iterations are repeated until all of the connected pixels that show some metabolic activity are set to 1. The rest of the data is assigned a value of 0 , and all of the unwanted anatomica l structures are removed. Fig. 2 . 2 (a) - (b) contains the PET segmentation results for the same patient shown in Fig. 2 .1. Fig. 1. 2 ( a) shows unprocessed PET slice numbers 6, 10, 14, 18, 22, 26, 30, 34, 38, and 42 in the axial plane, which correspond to the ten CT slices shown in Fig. 2.1. Fig. 2. 2 (b) shows that all of the unwanted structures are removed. 25 (a) Unprocessed PET slice numbers 6, 10, 14, 18, 22, 26, 30, 34, 38, and 42. (b) Segmented PET slice numbers 6, 10, 14, 18, 22, 26, 30, 34, 38, and 42 . Figure 2 .2 : The segmentation results for the PET images, where (a) shows the unprocessed PET slices in the axial plane, and (b) shows the same PET slices after the images are segmented . T he selected axial slices are evenly distributed with in the 47 s lice dataset. Even with significant difference s in the shape of the brain structure among these slices, the seg mentation process performs well in each slice . 26 2.4 PET/CT Brain Registration 2.4.1 Preprocessing Before the PET and CT images are registered, both dataset s are resized using the DICOM header information such that, for each pixel in the PET data, there is a corresponding pixel in the CT data. For the CT images , the pixels are expanded from 0.9766mm to 1mm on each side , and for the PET images the pixels are m ade smaller by 3.27mm to 1mm on each side . Both dat asets are cropped to show only the b rain region in order to reduce the processing time. Once the images are cropped , the Canny edge detection algorithm [62] is applied to calculate the contours of the PET and CT brain s . The registration process is carried out in two steps, where one step accounts for the shifting of the head, and the other step accounts for the rotation of the head during data acquisition . 2.4.2 Translational Registration To align the CT and PE T images, the centroids of the segmented brain s from the two modalities are calculated. For this purpose, t he centroid is defined as the center point of the brain which lies in the center of the x, y, and z axes with respect to the brain pixels. Once the c entroids are aligned, PET and CT image alignment is improved through translationa l registration . If there is no rotation of the head during the exam, then the datasets will be registered correctly when the ce ntroids of the PET and CT brain are aligned . If the head rotates , translational registration alone is insufficient , and an additional rotation of the CT attenuation correction map is also required , which is explained in the following section. There are four different cases for the translational re gistra tion which are as follows: 27 1. There is no motion between the PET and CT scan s . 2. There is only a linear shift of the head position along one or more axes between the scans . 3. O nly rotation of the head occurs between the two scans . 4. B oth types of misal ignments occur . In the first case, wh ich is the ideal scenario, there is no motion of any kind, and the cen ter of the cropped PET data exactly o ccupies the same coordinates as the center of the CT data . As a result, the edges of the PET brain coincide wit h the edges of the CT brain. In this case , the output of the automate d registration software yield s the original CTAC. In the second case, only linear motion of the head occurs , which means that the CT data is shifted along one or mo re axes. The shift s al ong the x, y and z axes are determined by calculating the distance between the ce nters of the PET and CT volumes. The CT images are then aligned with the PET images ba sed on the shift values calculated for the x, y, and z directions . Since there is no rota tion of the head i nvolved in this case, when the CT images are shifted, the edges of the CT brain will coincide with the edges of the PET brain and the two modalities will be aligned. In the third case, only rotational motion of the head occurs , so even t hough the centroid s of the PET and the CT data are already aligned, the edges of the PET and CT brains do not overlap. Therefore, rotational registration is required which is explained in the next section. 28 For the last case, the steps in the previous two c ase s are combined. First, translational registration aligns the centers of the PET and CT cropped regions , which gives the shifts along the x , y and z axes. This is followed by rotational registration , which completes the alignment of the PET and CT brain structures. 2.4.3 Rotational Registration During a PET/CT exam, the patients generally have some difficult y stay ing still throughout the procedure. In most cases, the patients rotate their heads along the x and y axes, compensate for these motions, additional rotational registration is required. To rotate the CT image in the sagittal plane, an objective function is defined such that the maximum penalty is assigned to the boundary of the brain along the sinus cavity. This section of the PET brain has the highest probability of a metabolic artifact if there is overlap with the sinus cavity of the CT image. The decision regarding the direction of the rotation is made based on the initial projection of the PET brain boundary along the sinus cavity. I f the brain region in the PET image is projected on to the sinus cavity in the CT image , then the rotation of the CT image is in the counter - clockwise direction, otherwise the CT image is rotated clockwise until the brain/sinus boun daries in the PET and CT images overlap with each other . This approach has worked well with every dataset tested thus far. In order to rotate the CT image in the axial plane, the translated PET brain contour is overlaid onto the CT image. The fused axial image is divided into four quadrants, where the origin coincides with the center of the brain. As before, t he center of the brain is approximated by averaging the locations of the non - zero pixels which correspond to the brain. In each quadrant, the average distance between the boundary of the PET brain 29 and the CT brain is calculated . If the PET brain boundary is located to the left of the CT brain boundary in the first and second quadrants and located to the right of the CT brain boundary in the third and f ourth quadrants, then the CT image is rotated coun ter - clockwise. Otherwise , if the PET brain boundary is located to the right of the CT brain boundary in the f irst and second quadrants and located to the left in the third and fourth quadrants, then the CT image is rotated clockwise. The rotation in the coronal plane is performed with a similar approach , which divides the image in to four quadrants and rotat es the CT image based on the distance s between the edges of the PET and CT brain images in each quadran t . 2.4.4 Image Registration Results Th e automated registration procedure described above is applied to data sets acquired from ten patients. In each dataset, the shift values and the rotation angles required to align the P ET and CT images are calculated, and t he results are listed in Table 2. 2 . The results show that the shift along the x and z axes is significant in some of the patients and that the mi salign m e nt along the y axis is consistently very small. No y axis shift occurs because, for this kind of misalignm ent, the patient has to lift his or her head from the table which is the least likely among all of the possible head motions prior to PET image a cquisition. The largest rotations were observed in the sagittal plane , where the average of the absolute value of the rotations was 3.5 degrees , followed by the rotations in the axial plane , where the average of the absolute value of the rotations was 2.5 degrees . Very little rotation of the head was observed in the coronal plane for all patients , where the average of the absolute value of the rotations was 0.4 degrees . 30 Table 2. 2 : R esult s of the PET and CT image registration . Translational Registration (mm) Rotational Registration (degrees) x - axis y - axis z - axis Axial Plane Sagittal Plane Coronal Plane Patient 1 9 0 12 5 10 0 Patient 2 - 2 0 0 0 0 2 Patient 3 3 0 0 0 - 5 0 Patient 4 0 0 0 0 - 5 0 Patient 5 5 0 3 5 0 2 Patient 6 0 0 6 0 - 15 0 Patient 7 - 3 2 0 0 0 0 Patient 8 5 0 3 10 0 0 Patient 9 0 0 3 5 0 0 Patient 10 6 2 6 0 0 0 Average of the absolute v alue 3.3 0.4 3.3 2.5 3.5 0.4 Fig. 2. 3 demonstrates the result of the regi stration process applied to PET and CT images in the axial, sagittal , and coronal planes. Fig. 2. 3 (a) shows CT slice number 33 in the axial plane with the brain contour from the co rresponding PET axial slice overlaid onto the CT image . The PET and CT brain structures show significant misalignment near the left boundary of the brain . Fig. 2. 3 (b) shows the brain contour from sagittal PET slice number 64 overlaid onto the correspondin g CT sagittal slice. Part of the PET brain lies outside of the top boundary of the CT brain, which indicates that patient movement occurred during the exam. Fig. 2. 3 (c) shows the PET brain contour overlaid onto the CT image for coronal slice number 64. In this case, the PET brain contour lies outside of the 31 left boundary of the CT brain, which is similar to the misregistration depicted in the axial slice shown in Fig. 2. 3 (a). Fig. 2. 3 (d - f) shows the result after translational registration is applied to the PET and CT images. Fig. 2. 3 (d) shows the brain contours from the PET image overlaid onto the corresponding CT image in the axial plane after the CT image is shifted to align with the PET image . Fig. 2. 3 (e - f ) shows the shifted CT image below the PE T c ontour i n the sagittal and coronal plane s , respectively . After the translational registration step is completed, the brain structures from the two modalities are still mis aligned. This is because ro tational alignment is also required . Fig. 2. 3 (g - i) shows the results after the PET contours and CT images are rotationally aligned. Fig. 2. 3 (g) shows an aligned PET brain contour overlaid on to a CT brain image in axial slice 33. After the images are rotationally aligned, the entire PET brain is loc ated inside t he CT brain. Fig. 2. 3 (h) shows the result of the rotational registration in the sagittal plane. By rotating the CT image in the sagittal plane, the misalignment near the si nus cavity is eliminated. Fig. 2. 3 (i) shows the result of rotational alignment in the coronal plane , which is consistently very small in all patients. The shift parameters are applied to the CT dataset instead of the PET images because the aligned CT attenuation correction (CTAC) map is required by the system for artifact - free reconstru ction of the PET images. 32 (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 2. 3: PET/CT image registration result s , where the white line s represent the PET brain contours and the gray scale image s show the CT brain. Fig. 3 (a - c) illustrates the original PET and CT data for slice number 33 in the axial plane, slice 64 in the sagittal plane, and slice 64 in the co ronal plane , respectively. Fig. 3 (d - f) shows the result s of translational registration in the axial, sag ittal and coronal planes. Fig. 3 (g - i) demonstrates a significant improvement after translational and rotational registration . 2.5 PET Reconstruction To demo n s trate the effects of PET/CT mis registration on the attenuation - corrected PET data, PET images were reconstructed with unregistered and the registered CTACs. The reconstructed PET images were compared in the brain region before and after registration. Among the ten patients included in this study, the PET and CT images from six patients had insignificant misregistration errors; therefore, no artifact was observed in 33 the reconstructed PET data using the unaligned and the aligned CTAC. For the remaining four p atients, there was a significant improv e ment in the reconstructed PET image when the registered CTAC was used. The results of the PET image reconstruction before and after registration are shown in Fig. 2. 4 for patient number 1. Among t he 10 patients, thi s patient contained the lar gest misregistration error, as shown in Table 2. 1 , where significant translational and rotational artifact s were observed in the PET brain image . To demo n strate the effect of PET/CT misregistration on the PET reconstruction , sele cted PET images in the axial, sagittal , and the co ronal planes are shown in Fig. 2.4. Fig. 2. 4 (a - c) shows the PE T slices reconstructed using the misaligned CTAC. The imag es in this figure show axial slice 33, sagittal slice 64, and coronal slice 64 , respe ctively. In the axial and coronal images, the left half of the PET brain contains a significant artifact d ue to erroneous attenuation correction with a misaligned CTAC. Similarly, the region of the PET brain image that is projected onto the sinus cavity i n the CT image also shows signs of diminished intensity as shown in Fig. 2. 4 (b). Once the PET and CT images are aligned and the PET data is reconstructed using the registered CTAC, the image artifacts are eliminated a nd the result is shown in Fig. 2. 4 (d - f). The entire PET brain image obtained after the PET and CT images are aligned shows uniform intensity that corresponds to uniform metabolic activity, indicating a healthy brain. 34 (a) (d) (b) (e) (c) (f) Figure 2. 4: Reconstructed PET images using misa ligned and aligned CTACs. Fig. 2. 4 (a - c) shows the reconstructed PET slices in the axial, sagittal, and the coronal plane s u sing the misali gned CTAC. Fig. 2. 4 (d - f) shows the same reconstructed PET slices in the axial, sagittal, an d coronal plane s using the aligned CTAC. The other three patients with notic e able m isregistration errors are patients 6, 8, and 10 in Table 2. 1 . Pa tient 6 has a z axis shift of 6mm and a rotational misregistration of 15 degrees clockwise. This patient does not demonstrate any x or y axi s shift or any rotation in the axial or coronal planes. Since the only misalignment is along the z axis and the only rotation for t his patient is in the sagittal plane, a sagittal slice (number 64) is selected to 35 demonstrate the registration and the reconstruction results . Fig. 2. 5 (a) shows the misaligned CT with an overlaid PET brain contour. Due to the rotation of the head in a overlaps with the sinus cavit y in the CT image . Fig. 2. 5 (b) shows the same C T sagittal slice after the CT image is aligned with the corresponding PET slice. The reconstruction of the PET data using the mis aligned CT AC, as shown in Fig. 2. 5 (c), demonstrates diminished metabolic activity in the brain region along the sinus cavity. This artifactual metaboli c defect is eliminated in Fig. 2. 5 (d) when the PET data is reconstructed using the aligned CTAC. 36 (a) (b) (c) (d) Figure 2. 5: PET image reconstruction using misaligned and aligned C TAC s for patient number 6. Fig. 2. 5 (a) shows sagittal slice number 64 of t he misaligned PET and CT images , Fig. 2. 5(b) shows the same sagittal slice after the PET and CT image s are registered, Fig. 2. 5(c) shows the reconstructed PE T image using the misaligned CT image , and Fig. 2. 5(d) shows the sagittal PET slice reconstructed using the aligned CTAC. 37 The PET and CT images for p atient number 8 are translationally misaligned by 5 mm along the x axis and by 3 mm along the z axis . These images are rotationally misaligned by ten degrees in the clockwise direc tion in the axial plane. The improvements in the alignment are especially evident in the axial plane, where axial slice number 24 is selected to show the registration and th e reconstruction results . Fig. 2. 6 (a) and (b) show the misaligned and aligned PET/CT images, respectively. Before the images are aligned, part of the PET brain in projected outside of the CT brain as shown in Fig. 2. 6 (a). This e rror is corrected after the t wo modalities are aligned as shown in Fig. 2. 6 (b ). Fig. 2. 6 (c) shows that PET images reconstructed with a misaligned CTAC produces an artifactual metabolic defect near the left boundary of the brain , whic h is eliminated when the PET images are reconstructed with the aligned CTAC as shown in Fig. 2. 6 (d). For the same patient, the registration and reconstruction results are shown for slice number 33 in Fig. 2.7, where the reconstructed images are shown usi ng a different colormap. Fig. 2.7 (a) and (b) show the misaligned and the aligned PET/CT images, respectively. Fig. 2.7 (c) shows the PET image that is reconstructed using the misaligned CTAC , which suggests that an abnormality is present in the left porti on of the brain. Fig. 2.7 (d) shows the reconstructed PET image obtained from the aligned CTAC , which shows no evidence of a brain abnormality. The fourth patient showing an example of a significant misregistration error is patient number 10 in Table 2. 1 . T he PET and CT images for t h is patient are translationally misaligned by 6 mm along the x axis, 2 mm along the y axis, and 6 mm along the z axis. There is no rotation al misalignment of the PET/CT images for this patient . The primary translational movement is along the x and z axes , where the ef fects of this motion are 38 clearly observed in the coronal plane . The registration and reconstruction results are demonstrated in coronal slice 64. Fig ures 2. 8 (a) and (b) show the misaligned and the aligned CTAC s with the corresponding PET brain contour s . Fig. 2. 8 (c) shows coronal PET slice 64 reconstructed using the erroneous CTAC , which demonstrates the effect of PET/CT image misregistration . T he misregistration artifa ct is removed when the software - aligned CTAC is u sed for the reconstruction of the PET image as shown in Fig. 2. 8 (d). 39 (a) (b) (c) (d) Figure 2. 6: R ec onstructed P ET images using misaligned and aligned C TAC s for patient number 8. F ig. 2. 6 (a) shows axial slice n umber 24 of t he misaligned PET and CT images , Fig. 2. 6(b) shows the same slice af ter the PET and CT images are registered, Fig. 2. 6(c) shows the reconstructed PE T image using the misaligned CT AC , and Fig. 2. 6(d) shows the axi al PET slice reconstructed using the aligned CTAC. 40 (a) (b) (c) (d) Figure 2.7 : Reconstructed P ET images using misaligned and aligned CTAC s for patient number 8. Fig. 2.7 (a) shows axial slice number 33 of the misaligned PET and CT images , Fig. 2.7(b) shows the same slice after the PET and CT images are registered, Fig. 2.7(c) shows the reconstructed PET image with the misaligned CT AC using the jet color map in Matlab , and Fig. 2.7(d) show s the axi al PET slice reconstructed with the aligned CTAC using the jet color map in Matlab . 41 (a) (b) (c) (d) Fig ure 2. 8 : Reconstructed PE T images using misaligned and aligned CT AC s for patient num ber 10. Fig. 2. 8 (a) shows coronal slice number 64 of the misaligned PET and CT images , Fig. 2. 8 (b) shows the same coronal slice af ter the PET and CT images are registered, Fig. 2. 8 (c) shows the reconstructed PE T image using the misaligned CT AC , and Fig. 2 . 8 (d) shows the sagittal PET slice reconstructed using the aligned CTAC. 42 3 Attenuation Correction of Cardiac Data 2 Cardiac images acquired with different imaging modalities provide complementary information. Therefore, the fusion of such multimodal datase ts can provide important support for a medical diagnosis in c ardiology. However, in clinical practice, the use of multimodal imaging techniques is limited due to the mis alignment of images acquired from different modalities . Recently, with the success of h ybrid scanners, the clinical need to merge complementary information in cardiac studies has been emphasized. These scanners are able to acquire multimodal data that provide s complementary information in a single image session . The mos t important examples o f hybrid imaging systems are PET/CT scanners [63 - 64 ], which are widely applied to cardiac imaging studies because of their ability to correlate coronary artery disease (CAD ) and myocardial perfusion provided by the CT and PET images , respectively . Although image acquisition in a single session generally minimi zes the misalignment between the PET and CT datasets, the spatio - temporal mismatch of ca rdiac datasets in particular is not completely resolved [65 - 68 ] . Thus , manual registration with integrated commer cial software is usually performed in cli nical practice to align the images [69 - 70 ]. For this reaso n, an automatic alignment method is potentially very useful for cardiac PET/CT image registration [ 71 - 73 ] . _________________________________________________ ____ 2 Reproduced from K. Khurshid, K. L. Berger, R. J. McGough, Respiratory Cardiac Motion Compensation in PET/CT for Accurate Reconstruction of PET Myocardial perfusion Images, Journal of Physics in Medicine and Biology , 53(20), 5705:5718, 2008 with the p ermission of Journal of Physics in Medicine and Biology. 43 3.1 Data Acquisition The PET/CT image acquisition protocol begins with the intravenous administration of 25 - 35 mCi of N - 13 ammonia at rest or after pharmacologic stress. The patient is positioned in th e scan ner, and the CT scan is performed with an acquisition field of view (FOV) of 50 cm. The reconstructed FOV for the CT has a default value of 50 cm, which is used for all p atients. The patient bed is moved to the starting position, and then the PET sca n is initiated. PET images are reconstructed with a field of view of 41.9 cm followed by a left shift of 4.0 cm within a 128 by 128 matrix [74] . The important parameters for PET and CT data acquisition are listed in Table 3. 1. The automated processing of t he PET and CT cardiac images is explained in the following sections . 3.2 Cardiac Image Segmentation PET images are averaged separately in the axial and sagittal planes t o estimate the location of the heart. Slice averaging in the axial plane is performed by c alculating the weighted average of each pixel in the z direction. Although unweighted averagi ng of each pixel, represented by Eq. 3.1, gives a fair estimate of the extent of the cardiac boundary, applying different weights with Eq. 3.2 to different intensi ty levels enhances the contrast between the high and low i ntensity regions to achieve better isolation of the cardiac region [75] . 44 Table 3. 1: Imag e acquisition parameters for PET/CT imaging system of cardiac patients . PET Resolution (pixels) 128 x 128 Reconstructed Field of View 419 mm x 419 mm Scan Distance along the z - axis 150 mm Slice Thickness 3.27 mm Bits per Pixel 16 Detector Material BGO Crystal Size 4.7 mm x 6.3mm x 30 mm CT Resolution (pixels) 512 x 512 Reconstructed Field o f View 500 mm x 500 mm Scan Distance along the z - axis 150 mm Slice Thickness 3.75 mm Bits per Pixel 16 Tube Voltage 140 kVp Tube Current Detector Type 40 mA LightSpeed16 HiLight Matrix II detector, polycrystalline ceramic 3.1 3.2 Equation s 3.1 and 3.2 contain expressions for computing unweighted and weighted averages at a single image location with coordi n ates (x,y), where f x,y and g x.y represent the input and the output pixel at the selected image location , respectively , and N represents the total number of slices averaged . In each processed image , if the pixel value is above th e threshold , then the selected weight is greater than one, and if the pix el 45 value is below the threshold , then the weight is set to one. Since most of the slices contain the heart in the PET dataset, the cardiac region is of significantly higher intensity than the liver after weighted averaging , so the heart is easily distinguished from the liver, which facilitates extraction of the heart from the PET data. The weighted avera ging in the axial plane indicates the upper and lower bounds of the cardiac region along the x and y axes. Averaging is also performed in the sagittal plane to calculate the z axis bounds for the cardiac region. The z axis bounds define the range of axial PET slices that are used for fuzzy clus tering of the heart , as described in section 3 .3. The weighted average in the axial plane is also used for maskin g, as described in section 3 .4 . Fig. 3.1 (a ) shows the averaged image using equal weights applied to all the intensity levels , whereas Fig. 3.1 (b) demonstrates better isolation of the h eart by applying variable weights based on the intensity value of the pixels , which improves the contrast between the low and high intensity values . The w eight in Eq uation 3.2 can be an abs olute value or the weight can be defined relative to the normalized intensity of the pixels. In the results above , a subjectively chosen value of five was selected for the weight, and a normalized threshold of 0.45 was selected between the low and high intensities. The objective of this averaging is to select only a few s lices in the sagittal plane and to ensure the presence of cardiac region in the selected slices. This technique provides the lower and upper bound s within whi ch the heart is present for the sagittal and the coronal planes . T he same averaging process is ap plied to the PET slices in the coronal plane . Fig. 3.3 shows the result s from unweighted averag ing (a ) and the results from weighted averaging (b ) in the coronal plan e . From these results , the lower and upper bounds of the cardiac slices in the axial plane are acquired , as shown in Fig. 3.4 . 46 (a) (b) Figure 3. 1: Averaging r esult s in the axial plane, where (a) shows the unweighted average and (b) shows the weighted average . Fig ure 3. 2: Averaging in the axial plane indicates which slices to p rocess in the sagittal direction . 47 (a) (b) Figure 3 .3 : Averaging r esult s in the coronal plane, where (a) shows the unweighted average and (b) shows the weighted average . Figure 3. 4: Averaging in the coronal plane indicates which slices to pr ocess in the axial direction. 48 3.2.1 Fuzzy Clustering Fuzzy c - mean clustering [76 - 77] extracts the geometries of the significant c lusters from the PET images. Fuzzy clustering is applied only to the selected axial slices, as defined by the extent of the cardia c region determined from weighted averaging . Applying fuzzy clustering only to the slices containing the heart greatly reduces the computation time. The mathematical expressions that are evaluated are given by and 3.3 , 3.4 w here, m ik i, c = total number of clusters , d ik = distance of point k to the center of cluster i, d jk = distance of point k to the center of cluster j , and q = fuzziness exponent . Fuzzy clustering obtains the largest clusters from the individual axial PET images that represent the heart and the liver. To separate the cardiac cluster from the other clusters, masking is used as described in the following section. 3.2.2 Masking Through masking, the cardiac region is isolated and all of the unwanted clusters are removed from the axial slices as shown in Fig. 3.5 . The mask is obtained from the weighted average in the axial plan e as described in section 3 .2, which is converted into binary form. By applying this mask, the boundary of the cardiac region is obtained, and 49 all of the unwanted cl usters are removed. After three steps are completed, i.e., estimating the car diac region, fuzzy clustering, and masking, the remaining PET images contain only the cardiac region . (a) (b) (c) (d) Figure 3.5: R esults of the pre - processing steps in the axial plane , where (a) shows unprocessed axial slice number 2 3 , (b) shows the image af ter fuzzy clustering is applied , (c) shows the binary mask , and (d) shows the extracted cardiac PET data . 50 The same process is applied to the sagittal slices to extract the cardiac cluster and the result is shown in Fig. 3.6. ( a ) (b ) Figure 3. 6 : R esult obtained after masking in the sagittal plane, where (a) shows the binary mask and (b) shows the extracted cardiac PET data . 3.2.3 Edge Detection The segmented PET images are first processed with a low pass filter that smooths out th e boundary of the heart. The Canny edge detection alg orithm [ 62 ] is then applied to obtain the boundary of the cardiac region . Gradients are calculated for the smoothed image in the x - and y - direction respectively with Eq. 3.5 and Eq. 3.6, which are given by 51 and 3.5 . 3.6 The approximate magnitud e of the gradient is calculated using Eq. 3.7 , and the direction of the gradients is calculated using Eq. 3.8 , |G| = | G x | + |G y | 3.7 - 1 ( | G y | / | G x | ) , 3.8 where G x and G y are the derivatives in the x and y directions, respectively. The approximate magnitude of the gradien direction of the gradient. Fig. 3.7 shows the results obtained with the se image processing steps evaluated o n a representative PET image in the axial plane . Fig . 3.7 (a) shows axial slice number 40 from the PET data, which consists of 47 slices. In Fig 3.7 (a), the high intensity regions are t he heart and the liver. Fig . 3.7 (b) shows the result after fuzzy clustering. The heart and liver clusters are clearly shown in this image. The liver region is removed from th e image us ing masking , as shown in Fig . 3.7 (c). The result of the edge detection performed on t he PET 52 image is shown in Fig. 3.7 (d). This edge information is used for the registration of the PET and CT images. After the PET contour s of the heart are obtain ed, the corresponding information is extracted from the CT images. First, each CT image is processed with a low pass filter to smooth out the cardiac region. Then, Canny edge detection is applied to the filtered images. The resulting image contains the edg es of the heart as well as other structures such as liver and ribs. To extract the cardiac contour from the CT image and eliminate the unwanted contours, the approximate center of the heart is determined by averaging the pixel coordinates of the PET contou r of the heart. Starting from this point in the CT image, the nearest edge at all angles is identified as the cardiac contour, and the remaining contours in the CT image are eliminated. Even for the largest misregistration observed between the two modaliti es, the center point of the PET heart is consistently located within the heart in the CT image , and the contour of CT heart is correctly identified. Once the preprocessing and segmentation is complete, the PET and CT images are registered with a low probab ility of error because all of the unwanted pixels have been removed from the data as shown in Fig. 3.8. 53 (a) (b) (c) (d) Figure 3 .7 : R esults of the pre - processing steps applied to the PET image, where (a) shows the original ax ial image, slice number 40 (z - axis coordinate 102.39 mm), (b) shows the fuzzy clustered image containing the cardiac cluster and the unwanted liver cluster, (c) shows the masked image in which the liver cluster is removed , and (d) shows the extracted conto ur of the cardiac region. 54 (a) (b) (c) (d) Figure 3.8: Result of the processed images in the sagittal plane, where (a) shows the original PET image, (b) shows the contour obtained from the processed PET image, (c) shows the original CT image, and (d) shows the contour obtained from the low - pass filtered CT image. 55 3.3 PET/CT Image Registration After a PET/CT scan, image registration is necessary to ensure accurate and consistent im age reconstruction. Although , the PET images may overlay accurately onto the CT images in some cases; however, in many other case s , the heart geometries extracted from the PET and CT data may not overlap perf ectly . In such case s , the reconstruction of PET using the CT can contain areas of false hypoperfusion. Although vo luntary motion can also be important , the main reason for the misalignment of the PET and CT images is the respiratory motion of the patient. Due to the moving diaphragm, the heart is displaced up to 2 centimeters along the long axis of the body during a r espiratory cycle [ 78 ] . T hus , the alignme nt of the heart can vary between scans . S ince the PET data is averaged over a 15 - minute interval, the position of the PET heart is also averaged over the entire respirator y cycle. However, CT images provide the insta ntaneous location of the heart during the respiratory cycle. S everal approaches can be used to eliminate this problem. One method take s multiple CT scans of the patient in diff erent respiratory phases and attempts to find the best match through visual insp ection. With this method , the patient go es through additional CT scans, which increases the radiation exposure. Another approach slow s the CT scan acquisition and average s over 1 - 3 respiratory cycles, but this still may not produce enough temporal averagin g to match the PET scan. Keeping this in mind, an automated method is developed that can take one CT and one PET scan and align the geometries of the heart using least squares automatic image registration. To ensure alignment for all three degrees of freed om, registration is performed on all three axes. This process is carried out in two steps. In the first step , t he PET and CT data is resized so that each pixel from the PET image has a 56 corresponding CT pixel. After resizing, e ach pixel in each PET and CT i mage is 1 mm by 1 mm. This step is necessary because of difference s in the resolution and the field of view (FOV) of the PET and CT images. The matrix size of the CT image is 512 by 512 pixels with a field of view of 50 cm by 50 cm, where the FOV is calcul ated by multiplying the image resolut ion with the pixel spacing. PET images are 128 by 128 pixels with a field of view of 419 by 419 mm. For the CT images, the pixel size is initially 0.9796 mm by 0.9796 mm , and for t he PET images, the pixel size is initia lly 3.27 mm by 3.27 mm . Once the image s are scaled so that the pixels are the same size for both modalities, the CT and PET contours of the heart are aligned as described in the following section. Depending upon the phase of respiratory cycle, the amount o f mismatch changes . When there is no respiratory motion , the two cardiac geometries are aligned with each other. To compensate for the respiratory motion, least square s minimization is applied to the edges of the PET and CT heart contours , and a motion vec tor is generated. This motion vector defines the shifts that correct for the displacement. The edges obtained from the CT correspond to the entire myocardium , whereas the edges obtained from the PET data correspond to the left ventricle. Thus, only the edg es corresponding to the anterior and lateral walls are used for image registration. These edges , which share a boundary with the left lung , correspond to the same walls of the left ventricle in both the PET and the CT images. Since the lung attenuation par ameters are the main source of the hypoperfusion artifact, aligning the PET and CT cardiac edges along these boundaries eliminates this problem. 57 The shifts in the x and y directio ns are determined from the axial plane images , and t he z axis shift is determ ined from the images in the sagittal plane. For the x axis shift, the PET and CT axial images are traversed horizontally from right to left, and the distance between the first CT edge pixel and the first PET edge pixel is calculated. This process is repea ted for all of the rows in the PET and CT axial images, and then an average distance between the pixels is calculated using the shift values for each row. This average value provides the shift required to align the PET and CT images along the x axis. The s ame process is performed for the average y axis shift by traversing the PET and CT axial images vertically from top to bottom for all of the columns. The distance between the first PET and first CT edge pixel for each column is calculated and then the aver age of these value s is computed. To calculate the z axi s shift, the PET and CT data is analyzed in the sagittal plane. The sagittal PET and CT images are traversed vertically from top to bottom for all of the columns, and the distance between the first PET edge pixel and first CT edge pixel is calculated for each column and then averaged. The process of calculating the shifts for the x, y, and z axes is then repeated a second time to refine the alignment. 3.3.1 Image Registration Results In the images below, som e of the results generated from selected case studies are shown. In some of these images, the respiratory motion effect is quite significant. The automated registration procedure worked quite well on all of the data sets that demonstrated image misalignmen t due to respiratory motion. The first set of images (Fig. 3. 9, 3.10 ) show examples before and after PET/CT image registration in the axial plane , which shows the PET/CT data in the xy plane . The second set of images (Fig. 3. 11 ) show examples before and a fter PET/CT image registration in 58 the sagittal plane, which shows the PET/CT data in the yz plane . The grayscale background in these images shows the anatomical information from the CT data, wherea s the overlapping white contour represent s the boundary of the left ventricle obtained after processing the PET data. \ (a) (b) Figure 3. 9 : Axial p lane slice 24 , (a) misregistered image, and (b) a fter the cardiac geometries are aligned with the automated registration proced ure . (a) (b) Figure 3. 10 : Axial Plane slice 3 3, (a) misregistered image, and (b) a fter the cardiac geometries are aligned with the automated registration procedure . 59 (a) (b) Fig ure 3. 11 : PET/CT registratio n results in the sagittal plane, where the top half portions of (a) and (b) are misaligned, and the lower half portions show the aligned images . 3.3.2 Analysis of PET/CT Image Registration The misregistration between the PET and CT images was characterized in 50 heart patients using the automatic registration software. Only patients with visual hypoperfusion in the cardiac region of the PET images were selected for this analysis. For each patient, the attenuation corrected (AC) PET images were registered with the CT data, and the shift values in the x, y, and z directions in Table 3. 2 were calculated. The shift values in the x direction are significant on both sides of the axis. The largest shift in the x direction 60 is 12 mm, and the smallest shift value is - 6 m m. In the y direction, most of the shift values are zero or close to zero. The shift values in the y direction range from - 12 mm to 6 mm. In the z direction, most of the shifts are negative, which indicates that the registration program shifts the CT data upwards along the z axis. The shifts in the z direction range from - 26.2 mm to 6.5 mm. At the end of Table 3. 2, the average shifts in the x, y, and z directions are shown. Among x, y, and z, the average shift in the z direction, 8.7 mm, is the largest, f ollowed by the average shift in the x direction, which is 4.1 mm. The smallest average shift is 2.1 mm in the y direction. The large shift along the z axis corresponds to the significant displacement of the heart along the long axis of the body due to the motion of the diaphragm during the respiratory cycle. Fig. 3.12 displays three histograms that show the dist ribution of the shift values in the x, y, and z directions. In Fig. 3.12(a), the distribution of shifts in the x direction is centered near 3 mm. Fi g. 3.12(b) shows the distribution of shifts in the y direction, which contains a peak at 0 mm , and very few values elsewhere. The distribution of shifts in the z direction in Fig. 3.12(c) contains a peak at - 6 mm, where the range of z shifts extends from - 26.2 mm to 6.5 mm. 61 Table 3. 2 : Shifts in the x, y, and z directions required to compensate for the misregistration betwe en the PET and CT images in fifty patients. No. Shift Values (mm) No. Shift Values (mm) X Y Z X Y Z 1 9.8 - 5.9 6.5 27 4.9 - 11.8 - 13.1 2 9.8 - 3.9 - 13.1 28 8.8 0 - 16.4 3 3.9 0 - 13.1 29 4.9 0 - 3.3 4 4.9 - 2.9 - 16.4 30 6.9 - 2 - 16.4 5 5.9 3.9 - 6.5 31 2 0 0 6 - 3.9 0 - 6.5 32 3.9 0 - 3.3 7 2 0 - 6.5 33 4.9 0 - 13.1 8 0 0 - 13.1 34 0 - 2.9 - 26.2 9 9.8 2.9 - 16.4 35 0 0 - 6.5 10 3.9 0 - 19.6 36 4.9 0 - 3.3 11 2 2.9 - 9.8 37 5.9 0 - 6.5 12 3.9 2 - 9.8 38 7.8 0 - 6.5 13 1 2 - 6.5 39 3.9 0 - 13.1 14 3.9 0 - 22.9 40 9.8 5.9 - 26.2 15 0 0 0 41 2.9 0 - 6.5 16 6.9 - 9.8 0 42 11.8 - 1 - 9.8 17 - 5.9 - 2.9 - 3.3 43 5.9 0 - 6.5 18 - 2.9 - 5.9 - 3.3 44 2.9 0 0 19 2 - 2 - 9.8 45 - 2 0 0 20 - 2.9 - 5.9 - 6.5 46 0 0 - 3.3 21 - 2.9 - 6.9 - 3.3 47 0 3.9 - 6.5 22 0 0 0 48 2 5.9 3.3 23 4.9 0 - 13.1 49 5.9 2.9 6.5 24 5.9 - 3.9 - 13.1 50 3.9 0 3.3 25 0 - 3.9 - 6.5 Mean 4.1 2.1 8.7 26 0 0 - 9.8 Std. Dev. 3.9 3.4 7.5 62 (a) (b) (c) Figure 3.12 : Distribution of the shift values due to the misregistration bet ween PET and CT images (a) in the x direction, (b) in the y direction, and (c) in the z direction. 63 3.4 PET Reconstruction The goal of this research is to register PET and CT images to accurately align the heart geometries of both modalities and to generate new shifted CT attenuation correction maps. Once the shifted CT attenuation correc tion map is created, the PET data is reconstructed using the new shifted CTAC. Since the re is no mismatch between the PET data and the new CTAC, the PET images do not contain any exampl es of artifactual hypoperfusion, so only the actual condition of the heart is depicted in the reconstructed PET image . In the results shown below , the patient had no cardiac abnormality, but the misalignment of PET and CT hearts produced an artifactual pe rfusion defect. Once the PET images are reconstructed using the new CTAC obtained from the automated alignment software , the result s show that the hy poperfusion observed in the anterior and lateral walls of the heart was caused by a misregistered attenuation correction map . Fig. 3.13 shows an example of unregistered and registered PET and CT images in the axial plane for patient 1 in Table 3. 2 along with the corr esponding reconstructed PET axial images. Fig . 3.13 (a - b) shows the PET cardiac contour from axial slice number 24 in a set of 47 slices overlaid onto the grayscale CT image, where the results are shown befo re a nd after registration. Fig. 3.13 (c - d) shows th e reconstructed PET images obtained from the unregistere d and registered CTACs. Fig . 3.13 (a) contains an example of an unshifted CT that projects the lateral and anterior region of the PET heart onto the lung and bone of the CT, respectively. In this examp le, the motion of the patient in the axial plane is most significant in the x di rec tion. When the CTAC in Fig. 3.13 (a) is used for PET image reconstruction, the regio n of the PET heart that is projected ou tside of the CT heart is incorrectly attenua ted, wh ich creates artifactual hypoperfusion in the reco nstructed PET 64 image as shown in Fig. 3.13(c). In Fig. 3.13 (b), the registered CT image with an overlaid PET heart contour is shown. After the images are registered, the entire PET heart is projected within t he cardiac boundary of the CT image , providing the correct attenuation values for PET image reconstruction and eliminating the hypoperfusion artifacts from the reco nst ructed PET image as shown in Fig. 3.13 (d). (a) (b) (c) (d) Figure 3.13 : Axial CT slice 24 of patient 1 from Tabl e 2 with an overlaid PET heart contour, where (a) shows misregistered PET and CT images; (b) shows the result after the cardiac geometries are automatically aligned by the registration software; (c) shows the PET image reconstructed using the misaligned CT image ; and (d) shows the same PET image reconstructed using the aligned CT image . In the figure above, t he hypoperfusion is significant in the anterolateral wall of the heart in the reconstructed PET image in (c), which occurs as a result of the erroneous 65 attenuation correction of the PET cardiac region with the lung parameters of the CT data . The reconstructed PET image in (d) shows uniform perfusion in the entire cardiac region, demonstrating that the artifactual hypoperfusion due to misalignment is eliminated. Fig. 3. 14 shows the reconstructed PET data using the original CT attenuation c orrection maps. In Fig . 3.14 (e - h) , the right half portion s of the images wer e attenuated i ncorrect ly , so artifactual hypoperfusion is observed in these regions. The amount of misregistration error is quite significant in this example, which shows a sig nificant false perfusion defect . In Fig. 3.15 , the reconstructed PET images ar e shown using the correctly aligned CTAC , which demonstrates normal cardiac perfusion. All of the slices (a) - (h) in Fig. 3.15 contain uniform intensity distribution s in the cardiac walls with no sign of a perfusion abnormality. 66 (a) (b) (c) (d) (e) (f) (g) (h) Figure 3. 1 4 : PET images reconstructed with a misaligned CTAC demonstrate artifactual hypoperfusion . (a) (b) (c) (d) (a) (b) (c) (d) Fig ure 3. 15 : The same PET data used in Fig 3.14, reconstructed using the aligned CTAC, indicate normal perfusion . 67 After th e PET and CT images are registered using the automat ed software, the PET images are reconstructed using the shifted CT attenuation correction map . Among the 50 patients listed in Table 3. 2, only two patients (number 15 and number 22) did not require any a lignment between the PET and CT data . In these patients, a perfusion defect was diagnosed in the c ardiac wall. For 22 out of the 50 patients, the reconstruction of the PET images with the aligned CTAC maps showed uniform perfusion throughout the cardiac region, and the hypoperfusion artifact was eliminated. For the remaining 26 patients, the hypoperfus ion was n ot eliminated despite using the registered CTAC for PET image reconstr uction. These patients were diagnosed with a perfusion defect in the cardiac wall. Therefore, for this collection of patients, the hypoperfusion observed in 44% of the unaligned PET images was the result of an artifact caused by the misregistration between the PET and CT data . This artifact, when present, was consistently eliminated with the automated registration software. 3.5 Polar map Representation of PET Cardiac Data In most cas es, instead of displaying all of the slices for the three dimensio nal cardiac data separately , represent ing all of the inf ormation in a single image with a polar map is preferred . The condition of the heart is quickly analyzed by looking at the polar map s o that any abnormality present in the heart is readily localized . The p ol ar map is generated from short - axis slices of the heart as shown in Fig. 3.16 . The slices consist of concentric circles of the cardiac wall with decreasing radius, where the largest c ircle corresponds to the base of the heart and the smallest circle corresponds to 68 the apex of the heart. These concentric circles are then merged in to a single image with the apex in the center and the base at the outer edge of the circle [79 ] . Fig. 3.6 ( a) shows the selection of the slices along the short axis of the heart. These sl ices contain the circular myocardial wall with increasing radius from the apex to the base of the heart as shown in Fig. 3.6 (c). These slices are divided into sectors , and t he polar map is generated by placing the se slices in concentric circles with apex of the heart at the center of the polar map as shown in Fig. 3.16 (c). An example with substantial misalignment between the PET and CT data is shown in Fig. 3.17. A significant portion of the PET cardiac region is projected onto the lung in the CT image because of patient motion. Figures 3.17 (a) and (c) show the misaligned PET and CT data whereas Fig ures 3.17 (b) and (d) show the PET overlaid onto correctly aligned CT data. P ol ar maps are generated for each of the reconstructed PET datasets using the misaligned CTAC as well as the aligned CTAC. These polar maps are shown in Fig. 3.18. The polar map in Fig. 3.18 (a) shows a major hypoperfusion artifact, whereas the polar map in F ig. 3.18 (b) shows normal perfusion throughout the cardiac region. 69 (a) (b) (c) Figure 3.16: A polar map is created from the short axis slices of the heart. 70 (a) (b) (c) (d ) Figure 3.1 7 : PET images in the axial plane reconstructed using (a) misaligned CT data and (b) aligned CT data. PET images in the coronal plane reconstructed using (c) misaligned CT data and (d) aligned CT data . (a) (b) Figure 3.1 8 : Polar map s of reconstructed PET data using (a) misaligned CT data , and (b) aligned CT data . 71 4 Optimal Respiratory and Cardiac Phase s 3 4.1 Introduction A significant limitation of CT - based attenuation correction of PET data is the misregistra tion between the two modalities. The CT attenuation map captures an instantaneous snapshot of the heart at specific respiratory and cardiac phase s , whereas the PET images are acquired over multiple respiratory and cardiac cycles , so the PET heart is avera g ed over a larger region. D ifference s in the temporal resolution along with patien t movement may cause misalignment between the cardiac boundaries of the PET and CT images , drastically reducing the accuracy of the at tenuation correction . When PET data is re constructed using an erroneous attenuation map , this causes misregist ration artifacts that create fal se areas of hypoperfusion i n the PET cardiac region, which are in turn projected onto the lung in the CT data . These areas of hypoperfusion can alter inter pretation and create false positive diagnosis of ischemia or infarction. M isregistration between the PET and CT data is a result of involuntary respiratory and cardiac motion s . The misregistration due to the respiratory motion is translational and can be corrected using aut omated registration software [80 - 81] . The registration software calculates the distance between the edges of the cardiac contours of the PET and CT image to generate a motion vector. The PET and CT data is aligned based on the magnitude and direction of the motion vector. _____________________________________________________ 3 Reproduced from K. Khurshid , K. L. Berger, R. J. McGough, Analysis of Multiple Cardiac Phases of CT for M aximal Overlap with PET Images , International Symposium on Applied Electromagnetics and Mechanics , USA, 2007, with the permission of IEEE. 72 However, correcting the misregistration due to the cardiac motion during a heartbeat cycle involves scaling of the heart. During a cardiac cycle , the size of the heart changes significantly from the systolic phase to the diastolic phase. To guarantee that the PET and CT cardiac regions c ompletely overlap, the CT needs to be acquired during the diastolic phase where the heart is the largest . If the CT data is acquired during the systolic phase, the CT heart is the smallest , so the CT heart will not cover the entire cardiac region in the PET data set . If this is the case, even w ith proper registration, a substantial portion of the PET cardiac region will be projected onto the CT lu ng , which will result in erroneous attenuation correction. 4.2 Evaluation of Multiple Respiratory Phase s To demonstrate that the registration results are independent of the respiratory phase of the CT scan , four CT attenuation correction (CTAC) maps were acqui red through an institutional review board (IRB) approved procedure and registered wit h the PET data. The PET images were subsequently evaluated before and after alignment. The CTACs were acquired after the patient was instructed to hold his breath at diffe rent stages of respiration [82 - 83] . For these exams, no additional respiratory monitoring equipment was used. Only verbal instructions were given to the patient, i.e., exhale normally and hold, exhale halfway through and hold, exhale as much as possible an d hold. The patient was also told to breathe normally between the different CT scans. 4.2.1 Data Acquisition Fo u r different CT scans (CTAC1 - CTAC4) were acquired for 24 patients at different phase s of the respiratory cycle. CTAC1, which was used for the initial attenuation 73 correction of the PET data, was acquired during normal tidal end expiration before the PET stress exam, where the patient breathes out normally. CTAC2 was obtained at normal tidal end expiration after the PET stress exam, which differs from CTA C1 due to muscle relaxation. CTAC3 was collected halfway through normal tidal end expiration, where the patient breathes out halfway and holds his breath. CTAC4 was obtained during forced end expiration, where the patient was asked to exhale as much as pos sible and then hold his breath. For all of these CTACs, the PET and CT images were automatically registered with the software described in section 3 .3 . 4.2.2 PET/CT Image Registration Results The results obtained without and with the automatic registration sof tware in the sagittal plane for the PET data and four dif ferent CTACs are shown in Fig. 4.1. In Fig. 4.1 (a - d), the cardiac contours of the PET image are superimposed onto the unregistered CTACs. Fig. 4.1 (a) shows the PET cardiac contour superimposed onto CTAC1, Fig. 4.1 (b) shows the PET cardiac contour superi mposed onto CTAC2, and Fig ures 4.1 (c) and (d) show the PET cardiac contour s on CTAC3 and CTAC4, respectively. In this example, CTAC1 has the smallest misregi stration error along the z axis (3 mm) am ong of all the CTACs, and CTAC4 has the second smallest error of 9 mm , along the z axis. CTAC2 has the second largest misregistration error along z of 12 mm, and CTAC3, shown in Fig. 4.1 (c), has the largest misregistration error of 18 mm along z. The misr egistration between the PET data and the four CTACs, which is predominantly along the z axis, differs because of the varying displacement of the heart at different phases of the respiratory cycle due to the motion of the diaphragm. Fig. 4.1 (e - h) shows the results obtained with the automated registration software for the different CT respiratory phases. Fig. 4.1 (e) shows 74 the registered PET contour and CTAC1, Fig. 4.1 (f) shows the registered PET contour and CTAC2, Fig. 4.1 (g) shows the registered PET cont our and CTAC3, and Fig. 4.1 (h) shows the registered PET contour and CTAC4. As shown in these figures, the automated registration process suc cessfully aligns the cardiac geometries in the PET and CT data regardless of the respiratory phase in which the CT scan was acquired. This result, which demonstrates that the software eliminates the misalignment due to respiratory motion, indicates that only one CT scan is required for every patient. Images are registered for 24 datasets conta ining one PET scan and fo ur CT scans. The m ean and standard deviations of the shift values required for all the CTACs are calculated and are listed in Table 4.1 , where the CT images in t he se datasets are acquired after the patient is instructed to hold his breath at different resp iratory phases. CTAC2, which is end normal expiration, was the closest to the average heart location in the PET data . Table 4.1 : Mean s and standard deviation s of the shift values required in the sagittal plane for multiple CTACs acquired at different res piratory phase s . PET Respiratory Phase Mean Shift (mm) Std. Dev. (mm) CTAC 1 Normal end expiration before PET stress exam 8.6 6.11 CTAC 2 Normal end expiration after PET stress exam 4.3 3.31 CTAC 3 Halfway through normal end expiration 9.49 7.86 CTAC 4 Forced end expiration 7.10 3.24 75 (a) (b) (c) (d) Fig ure 4.1 : C ontours of PET cardiac images superimposed onto the four CTACs evaluated in the sagittal plane, slice number 78 (y=63.5 mm), before alignment. The results before registration are sho wn for (a) end normal expiration acquired before the PET stress exam (CTAC1), (b) end normal expiration acquired after the PET stress exam (CTAC2), (c) halfway through normal end expiration (CTAC3), and (d) forced end expiration (CTAC4). 76 (a) (b) (c) (d) Fig ure 4.2 : C ontours of PET cardiac images superimposed onto the four CTACs evaluated in the sagittal plane, slice number 78 (y=63.5 mm), after alignment. The results after registration are shown for (e) end normal expiration acquired before the PET stress exam (CTAC1), (f) end normal expiration acquired after the PET stress exam (CTAC2), (g) halfway through normal end expiration (CTAC3), and (h) forced end expiration (CTAC4). 77 4.2.3 PET Image Reconstruction Results To demonstrate the effe ct of misregistrat ion, PET slices in the sagittal plane are reconstructed using unregistered and regi stered CTACs are shown in Fig. 4.3 and Fig. 4.4 , respectively. These PET images are from the same sagittal plane shown in Fig. 4.1 and Fig. 4.2 . A consistent window - level is applied to all of the images to enhance the contrast between the normal and the hypoperfused cardiac regions. The window extends from 1 2 0 to 225 in all of the images, where the values in the original images range from 0 to 255. Fig. 4. 3 (a - d) shows the re constructed PET image usin g the unregistered CTACs. Fig. 4.3 (a) indicates that unregistered CTAC1 has a small misregistration error with respect to the PET image; therefore, the reconstructed PET image using the unregistere d CTAC1 in Fig. 4. 3 (a) does not show a significant hypoperfusion artifact. Fig. 4.3 (b) and Fig. 4.3 (c) contain PET images that are reconstructed using unregistered CTAC2 and unregistered CTAC3, respectively. Due to the large misregistrat ion errors between the unregistered PET and CTAC s 2 and 3 as shown in Fig. 4.1 (b - c), the reconstructed PET image shows significant false hypoperfusion in the a nterior wall , which is caused by the projection of the PET cardiac region onto the lung in the CT attenuation correction map. Fig. 4.3 (d), whic h shows the reconstructed PET image using unregistered CTAC4, again shows the hypoperfusion artifact in the anterior cardiac wall, but this artifact is not as significant as in Fig. 4.3 (b) and Fig. 4.3 (c). Fig. 4.4 (a - d ) shows the reconst ruction of the s ame PET image in the sagittal plane using the registered CTACs. All four of these reconstructed PET images show a uniform intensity distribution in the cardiac wal l with no sign of the hypo perfusion artifact. When 78 the results from Fig. 4.3 (a - d) and Fig. 4 .4 (a - d ) are compared , the importance of PET/CT im age registration is clearly demonstrated . With a misaligned CT attenuation correction map, the cardiac region of the reconstructed PET image shows a significant hypoperfusion artifact. By aligning the cardi ac geometries of the acquired PET and CT data, the hypoperfusion artifact is eliminated from the reconstructed PET images. 79 (a) (b) (c) (d) Figure 4. 3: S agittal slice 78 (y=63.5 mm) of the PET data reconstructed using unregistered CTACs. Results of PET reconstruction are shown for (a) unregistered CTAC1, (b) unregistered CTAC2, (c) unregistered CTAC3, and (d) unregistered CTAC4. 80 (a) (b) (c) (d) Fig ure 4.4 : S agittal slice 78 (y=63.5 mm) of the PET data reconstructed using registered CTAC s. The reconstructed PET results are shown for (a) registered CTAC1, (b) registered CTAC2, (c) registered CTAC3, and (d ) registered CTAC4. Fig. 4.4 (a - d ) indicates that the perfusion is normal in the entire cardiac region and that the hypoperfusion was an artifact produced by the unregistered CT images. 81 4.3 Validation of the Optimal Cardiac Phase PET/CT misalignment due to the incorrect cardiac phase at which the CT data is acquired cannot be corrected using image registration techniques due to significant redu ction in the size of the heart in the CT data. To maximize the overlap in the cardiac region for the PET and CT data, the CT images must be acquired at the diastolic phase when the size of the heart is the largest. If the CT data is acquired during the sys tolic phase when the CT heart is the smallest , t he PET and CT cardiac region s will not overlap completely . For CT images acquired during the systolic phase , despite image registration, a major porti on of the PET cardiac region is projected onto the lung in the CT data , so the reconstructed PET data will be attenuated incorrectly. 4.3.1 Data Acquisition Ten consecutive patients (7 men, 3 women) who were referred to our institution for a PET/CT exam were selected for this study. There was no prior knowledge of a ny hypoperfusion defects in the selected patients. The average age of this group was 61 years with a standard deviation of 7 years. The data from these patients was used to estimate the diastolic cardiac phase for the CT images that achieve maximum overlap with the PET cardiac region. PET and CT images were acquired with a GE Dis covery STE fusion PET/CT imaging system with a helical 16 row CT scanner at one end and a full ring PET tomograph with crystal size of 4.7 mm x 6.3 mm x 30 mm at the other end . T he CT scanner uses a tube current of 40 mA and a tube voltage of 140 kVp. The acquired CT data consists of 47 slices wit h a resolution of 512 by 512. T he reconstructed field of view for the CT images is 500 mm by 500 mm. The CT data is cardiac gated using an ECG system [84] . CT data 82 acquisition is initiated by the QRS peak of the ECG signal , and the data is binned into 10 equally spaced intervals called phases. To minimize the effects of breathing motion, the end expiration respiratory phase is selected f or the CT acquisition due to the smaller misregistration error on average with the PET data than any other respiratory phase. The PET data consists of 47 slices with a resolution of 128 mm by 128 mm . T he reco nstructed field of view for the PET images is 419 mm by 419 mm. 4.3.2 Maximizing the PET/CT Cardiac Overlap T o maximize the overlap in the cardiac re gion for the PET and the CT data, two different approaches are used. In the first approach, the maximum intensity projection for all of the co rresponding coordina tes from ten CT volumes is calculated. The noise pixels can play an important role in the resulting CTAC and therefore can introduce attenuation artifacts in the reconstructed PET images. The second approach takes the average of all the corresponding p ixe ls of the CT volumes from ten bins. Averaging the pixels can greatly affect the attenuation parameters , especially along the heart and lung boundary where the average value of the attenuation correction parameter can create artifactual hypoperfusion in the reconstructed cardiac region. Both of these approaches require multiple CT acquisitions over one cardiac cycle , which increases the radiation dose for the patient. To minimize the attenuation artifacts due to averaging and m aximum intensity projection, t en cardiac phases from several patients are analyzed to estimate the diastolic phase in which the heart is at the maximum size. By selecting th e diastolic phase, t he average intensity projection and the maximum intensity projection technique s are avoided, which reduces attenuation artifacts. The results show that , among the ten equally spaced 83 CTACs in a cardiac cycle, the 7th bin (i.e., 70% phase) captures the heart at the maximum size , where this phase overlaps the PET cardiac region more than any of the o ther phases. The 30% phase corresponds to systole , and at this phase , t he CT heart is the smallest . Onc e the phase corresponding to diastole is calculated, i.e. , 70% of the ECG cycle, the CTAC is acquired only at that particular phase , and the CT scanner r emains off for th e rest of the cardiac cycle. Thus, radiation dose to the patient is signifi cantly reduced without negatively impacting the reconstruction results for the PET data. 4.3.3 Methodology Average Intensity Calculation To generate the average intensi ty CT attenuation correction map , the corresponding pixels for all of the CT datasets, which are acquired at different phases of the cardiac cycle, are averaged together to genera te a single CT dataset. The drawback of this approach is that some of the car diac region in the diastolic phase projects onto the lung in the systolic phase , so some regions in the image are assigned the averaged value of the heart and lung. Therefore, an error is introduced in the value of the attenua tion parameter obtained from t he CT images, which creates artifacts in the reconstructed PET data. Fig. 4.5 shows a CT attenuation map generated from the average values of all pixels at a given coordinate . 84 Figure 4.5: CT attenuation map generated by averaging all of the CT datasets o btained at different cardiac phases. Maximum Intensity Projection In the approach that uses the maximum intensity projection , the maximum values at all of the corresponding pixels in all of the phases are found, and a new CTAC with these maximum values is generated. This process alters the entire CT dataset, and slight movement of the patient changes the output greatly by assigning high attenuating parameters of bones to other objects like heart, muscle, and fat . Fig. 4.6 shows an example of a CT attenuati on map that is generated using the maximum pixel value at each coordinate. 85 Figure 4.6: CT attenuation map generated by taking the maximum value of each pixel from all of the CT datasets obtained at different cardiac phases. Diastolic Phase Estimation T o avoid the problems in the two approaches described above , the CT scan in the diastolic phase is used for attenuation correction . Instead of processing the CTAC s and generating an altered CT attenuation map , the CT data is acquired during the diastolic ph ase in which size of the heart is the largest . The result ing CTAC maximally over laps with the PET heart while providing the smallest error for PET image reconstruction. With this approach, t he CT scans are a c quired in ten equally spaced cardiac phases that are binned over a cardiac cycle. Since the cardiac gating is triggered by the contraction of the right ventricle, the exact phase of diastole is unknown. This method is used to compare all of the phases acquired over the cardiac cycle, and then the diasto lic phase is found, which differs slightly from patient to patient. If the sampling interval between the phases is small, the exact location of the diastolic phase can be found for every dataset. O therwise , the nearest sampled phase is selected. 86 To determ ine which cardiac phase corresponds to diastole , where the heart is the largest , all of the CT datasets are segmented to obtain the cardiac boundary. Once the cardiac region is defined, the volume of the heart is calculated in all of the phases. To calcula te the volume of the heart, the pixels in the cardiac region are counted in each of the segmented volumetric dataset s . These pixels are then multiplied by the pixel spacing and the slice thickness to estimate the volume of the heart. Once the volumes are c alculated for each cardiac phase, the phase with the maximum volume is selected to represent diastole , and the phase with the smallest heart volume is selected to represent systole. 4.3.4 R esults The estimation of the diastolic phase is then validated through i mage fusion , which combines the PET data with the CT data from different cardiac phases . After image fusion, the pixels in the PET heart that are projected onto the lung in the CT data are calculated for each CT phase. Results show that the estimated diast olic CT phase maximally overlaps with the PET cardiac region , demonstrating the least amount of misalignment error between the two modalities . Thus, the diastolic phase is optimal for the reconstruction of the PET images. The PET/CT registration results ar e shown in Fig. 4.7 for two different CT cardiac phases. Fig. 4.7 (a - b ) contains the contour of the heart from the PET data superimposed on to the 30% and 70% CT cardiac phase s . The degree of misalignment between the CT and PET data depends on the size of t he heart, which is based on the cardiac phase in the ECG cycle. The CT data at the diastolic phase overlaps almost the entire PET heart as shown in Fig. 4 .7 (a ). In the systolic phase, the misalignment error is greater due to the smaller size of the c ardia c region in the CT data as shown in Fig. 4 .7 (b). The main difference 87 between the two phases is observed near the anterolateral wall of the heart. Some of the PET cardiac contour is projected onto the lung from the systolic CT image, wh ereas the entire PET cardiac contour is projected onto the CT heart from the diast olic phase. This was demonstrated in experiments performed with several data sets obtained from different patients. The results show that the 70% phase of the cardiac cycle , which corresponds to the diastolic phase in the CT data , is optimal for the attenuation correction of PET data . 88 (a) (b) Figure 4.7: C ontours of the PET image overlaid onto the corresponding CT image at different cardiac phases : (a) the 7 0% cardiac phase , which cor responds to dias tole, and ( b ) the 3 0% cardiac phase , which corresponds to sy stole. 89 The registration of the PET cardiac region with the corresponding CT cardiac region in the sagittal plane is shown in Fig. 4.8. Fig 4.8 (a) shows the CT heart in the diasto lic phase, where the entire PET cardiac contour is contained within the heart in the CT image . Fig. 4.8 (b) shows that the size of the CT heart in the systolic phase is much smaller and therefore does no t contain the complete PET cardiac contour , which mea ns that false attenuation parameters are assigned for PET image reconstruction. This misalignment cannot be corrected using image registration , so attenuation artifacts are expected in the reconstructed PET data if the CT images acquired during the systoli c phase are used for PET image reconstruction . (a) (a) Figure 4.8: PET cardiac contours in the sagittal plane registered with the co rresponding CT images acquired during (a) the diastolic phase and (b) the systolic phase . 90 4.3.5 Analysis of Un gated a nd End - Diastolic CTAC s For ten patients , the misalignment between the PET data and two CTACs was determined . The first CTAC was acquired at the end - expiration phase of the respiratory cycle with no cardiac gating. The second CTAC was acquired at the end - e xpiration and end - diastolic (ED) phase of the cardiac cycle. T he total shift values (Euclidian) were calculated manually by four users for the ungated CTAC and the end - diastolic phase CTAC. For each patient , the shift values were calculated in the axial, coronal, and the sagittal plane by four users. The total Euclidean shifts were calculated by determining the shift distances in all three planes. The value of the Euclidean shift was calculated by averaging the values provided by the four users . Table 4.2 lists the mean and standard deviations of the shift values for the two types of CTACs for each patient. The m ean shift required for the un gated CTAC was 16.8 mm with a standard deviation of 2.4 mm. F or the end - diastolic CTAC , the mean shift value was 10. 1 mm with a standard deviation of 1.9 mm. O n average, the end diastolic CTAC required a smaller shift to align with PET data . The largest shift required for the un gated exam was 29.1 mm, whereas the largest shift for the end - diastolic exam was 23.7 mm. A c omparison between the results obtained with the un gated CTAC and the end - diastolic CTAC reveal that , due to the larger size of the heart in the end - diastolic phase, the overall misalignment between the PET data and the CTAC is reduced. 91 Table 4.2 : Aver age shift values required for ungated CTAC and the ECG gated end - diastolic CTAC . Ungated CTAC End Diastolic CTAC Patient Mean Shift (mm) Std. Dev. (mm) Mean Shift (mm) Std. Dev. (mm) 1 10.5 1.4 7.1 2.0 2 8.7 2.6 5.1 3.1 3 14.8 1.4 7.7 2.7 4 29.1 3.9 23.7 1.4 5 9.9 3.6 1.5 1.0 6 15.1 2.0 12.0 0.9 7 28.4 3.2 10.7 2.7 8 15.9 1.9 3.6 2.1 9 11.8 1.6 11.7 0.7 10 23.4 2.6 17.7 2.7 Avg. 16.8 2.4 10.1 1.9 Max. 29.9 3.9 23.7 3.1 Min. 8.7 1.4 1.5 0.7 4.3.6 PET Image Reconstruction PET images are reconstr ucted using both the diastolic and the systolic phase CT attenuation correction maps. The result ing PET images in the sagittal plane are shown in Fig. 4.9. When the PET images are reconstructed using diastolic phase CTAC s , the correct attenuation parameter s are assigned throughout the PET cardiac region , which show s uniform perfusio n throughout the myocardium as demonstrated in Fig. 4.9 (a). In contrast , Fig. 4.9 (b) shows that the PET cardiac region near the anterior wall uses an 92 incorrect attenuation para meter that produces false regions of hypoperfusion in the reconstructed PET images . (a) (b) Figure 4.9: Sagittal P ET slice reconstructed using (a) a diastolic phase CTAC and (b) a systolic phase CTAC. 93 5 Manual vs . Automated Registration 5.1 Introduc tion In P ET/CT imaging , the alignment of the two modalities is important because misalignment can cause hypoperfusion artifacts that can potentially result in a diagnostic misinterpretation . For cardiac applications of PET/CT imaging, this misalignment is caused by patient motion and involuntary physiological movement of the organs. Certain steps are taken in order to minimize the patient motion, such as, (a) verbal instructions to the patient to stay still; (b) making sure that the atient is in a comfortab le position before data acquisition starts ; (c) having patients empty their bladder before the study begins ; and (d) using head holders and restraining tape for brain imaging [42,56]. However, the misalignment caused by differences in the position and size of the heart between CTAC and PET data acquisitions attributable to the following factors is unavoidable : - Cardiac displacement during respiration - Cardiac phase/volume mismatch due to contraction of the heart - Possible cardiac movement due to pharmaco logic stress - Temporal averaging which occurs over the length of the PET data acquisition Commercially available applications can assess and manually correct the misalignment between the PET and CT data . The goals of this study were to investigate the pro blem of CTAC misalignment in cardiac PET imaging, validate the effectiveness of automated registration with manual alignment , and calculate the variations in the registration results performed manually by multiple people . 94 5.2 Data Acquisition The images were a cquired using the Discovery ST E PET/CT system (GE Healthcare). Ten patients with a high degree of visual CTAC misalignment in either the rest exam or the stress exam were selec ted out of 25 total patient s . The acquisition parameters for the PET and the CT data are listed in Table 5.1. Table 5.1 : Image acquisition parameters for the PET/CT system . PET Resolution (pixels) 128 x 128 Reconstructed Field of View 419 mm x 419 mm Scan Distance along the z - axis 150 mm Slice Thickness 3.27 mm Bits per Pi xel 16 bits CT Resolution (pixels) 512 x 512 Reconstructed Field of View 500 mm x 500 mm Scan Distance along the z - axis 150 mm Slice Thickness 3.75 mm Bits per Pixel 16 bits 5.3 Manual Registration Process Using the GE Healthcare PET/CT visua l alignment application, t he selected exams were manually registered . Four users with varying experience registered th e PET and CTAC data from each exam. The PET and CTAC images were loaded into the A ttenuation Correction Quality Control ap plication (ACQC, GE Healthcare), and each user performed 95 visual alignment of the left ventricle activity in the PET image with the CTAC . Axial, coronal, and sagittal shift vectors were rec orded for the alignment of the CTAC by each user. The manual alignment procedure is outlined below. T he users were asked to ensure that all LV PET activity in the original image reconstructions is contained within the cardiac tissue i n the CTAC, but users were not coached during the shifting process. The instructions were as follows: 1) M ake any necessary adjustments , i.e. contrast adjustment and image scaling , for optimal vie wing of the fused images. 2) Align the PET and CTAC data sets first in the sagittal plane , then axial , and lastly the coronal plane . Since the primary direct ion of resp iratory motion is along the long axis of the body , the vertical axis in the sagittal plane was the expected direction of largest shift. W e determined that , based on the artifacts observed, overcorrection is better than undercorrection during manual regi stration of the PET and CTAC data . In particular, making sure that all of the left ventricle ( LV ) activity is contained within the cardiac tissue is preferred over leaving some PET activity aligned with lung in the CTAC. Also, care should be taken to ensur e that operators are well - trained in manual alignment techniques and that they understand the potential pitfalls. Fig. 5.1 shows the misaligned PET and CT image where some portion of the left ventricle of the PET heart is projected onto the lung in the CT image . The red lines represent the lines of response (LOR) which are greatly affected by the misalignment. These lines of 96 response for the left ventricle activity do not pass through cardiac tissue in the CTAC. PET image reconstruction performs attenuation correction as if photons originating from the left wall of the left ventricle passed through only lung/air, resulting in underestimated PET values for the region in the left ventricle which contains artifactual hypoperfusion. The t hickness of the myocardi al wall is most impacted by such lines that run parallel to the wall. Some lines of response , however, remain relatively unchanged by the CTAC shift , as shown by the blue line in the figure. Fig. 5.2 shows the reconstructed PET images before alignment . Fi g 5.2 (a) shows the long axis slice of the reconstructed image. The cardiac wall along the lung shows the most significant artifact. Fig. 5.2 (b) shows the short axis view of the reconstructed image. The polar map image is shown in Fig. 5.2 (c), with hypop erfusion visible in the anterolateral region. Fig. 5.3 shows the result that is obtained after manual alignment is applied to the axial images. The lines of response which were represented in red in Fig. 5.1 ar e now represented in green . These lines of re sponse pass through the cardiac region after alignment, therefore the correct attenuation parameters are now assigned to the PET data. Fig. 5.4 shows the reconstructed PET images after manual alignment. Fig. 5.4 (a) and (b) show the reconstructed PET imag es along the long axis and the sho rt axis , respectively. The cardiac region shows uniform perfusion throughout the entire myocardial wall. The corresponding polar map for the reconstructed PET data is shown in Fig. 5.4 (c). 97 Figure 5.1: Left ventricle a ctivity in the PET image misaligned with the lung in the CT ima g e . Many lines of response (LOR) for the left ventricle activity do not pass throu gh cardiac tissue in the CTAC. PET image reconstruction performs the attenuation correction as if photons origi nating from left wall of the left ventricle passed through only lung/air. (a) (b) (c) Figure 5.2: Reconstructed PET images using a misaligned CTAC , along (a) the long axis, (b) the short axis, and (c) the corresponding polar map. 98 Figur e 5.3: Left ventricle activity in the PET image that is manually aligned with the cardi ac region in the CT image resulting in accurate attenuation correction in the left ventricle . In this image, since the l ines of response originating in the cardiac regio n in the PET data pass through the corresponding cardiac region in the CT data, the correct attenuation parameters are assigned during the reconstruction of the PET data . (a) (b) (c) Figure 5.4: Reconstructed PET images using a manually al igned CTAC , along (a) the long axis, (b) the short axis, and (c) the corresponding polar map . 99 5.3.1 Quantitative Analysis of the Shift Values The mean and the standard deviation of the shift values obtained from the alignment results for the ungated CTAC s an d the end - diastolic (ED) CTAC s were calculated . The shift values are listed in Table 5.2. The m ean shift required for the ungated CTAC s was 15.7 mm with a standard deviation of 6.9 mm. F or the end - diastolic CTAC s , the mean shift required was 10.5 mm with a standard deviation of 6.1 mm. The size of the heart is maximized in the end - diastolic CTAC , so much smaller shift s are required on average to align with the PET data. The magnitude of the largest shift req uired for any exam was 32.9 mm. The m ean shift s i n each direction for the ungated CTAC s and the end - diastolic CTAC s for all users over all exams are listed in Table 5.3 . The most prominent shift was in the axial plane . For the gated CTAC s , the sagittal plane received the largest shift reduction compared to the standard CTAC shifts. To assess whether the g ated and s tandard CTACs generated substantially different results after shifting, the polar plots from the largest user shift with the standard CTAC were quantitatively compared to those from the largest user shift with the g ated CTAC. In the polar plot s, the maximum difference in any region was 9%, and the average difference was 5%. Out of all regions (20 exams x 5 regions), 11% of these had a difference greater than or equal to 5%. 100 Table 5.2: Av erage shift values for the manual alignment. Standard CTAC/End - Expiration End - diastolic CTAC/End - Expirat ion Patient Rest/Stress Mean(mm) Std Dev (mm) Mean (mm) Std Dev (mm) 1 Rest 11.4 1.5 8.5 2.2 Stress 10.5 1.4 7.1 2.0 2 Rest 7.3 1.0 4.2 1.7 Str ess 8.7 2.6 5.1 3.1 3 Rest 16.6 3.0 11.2 3.4 Stress 14.8 1.4 7.7 2.7 4 Rest 29.0 3.0 20.1 2.2 Stress 29.1 3.9 23.7 1.4 5 Rest 10.6 3.1 3.2 2.7 Stress 9.9 3.6 1.5 1.0 6 Rest 16.1 2.6 14.2 2.2 Stress 15.1 2.0 12.0 0.9 7 Rest 7.2 2.0 19.8 4.2 S tress 28.4 3.2 10.7 2.7 8 Rest 14.5 2.2 4.7 2.8 Stress 15.9 1.9 3.6 2.1 9 Rest 8.4 3.4 11.3 2.9 Stress 11.8 1.6 11.7 0.7 10 Rest 20.4 7.1 16.3 6.5 Stress 23.4 2.6 17.7 2.7 Mean Rest 14.1 2.9 11.3 3.1 Stress 16.8 2.4 10.1 1.9 Mean All Exams 15. 5 2.7 10.7 2.5 Table 5.3: Average shift values required in each plane. Axial Plane Coronal Plane Sagittal Plane Un gated CTAC 9.1 mm 3.1 mm 6.7 mm End Diastolic CTAC 6.7 mm 1.7 mm 2.6 mm 101 5.3.2 User - Dependent Shift Variations To quantitatively assess the im pact of the user variation in manual PET/CTAC shift s on the resulting PET images, reconstructions were generated using the smallest and largest manual shift magnitude s for each exa m. The goal of this assessment was to capture the extremes in the user varia tion for the manual CTAC alignment, focusing on cases where the shift difference was significant relative to the resolution of the PET imaging system. CardIQ Physio (GE Healthcare) was used for visualizing and comparing the images that were obtained from d ifferent CTAC shifts. The surface detection algorithm in CardIQ Physio automatically segmented the left ventricle. This segmented volume then provided the input for the polar plots. Polar plots were compared quantitatively after they were divided into 5 s ectors. C hanges in activity were then detected in the anterior, posterior, septal, and lateral regions of the left ventricle . Percentage scores for each region were computed based on the mean activity in each sector divided by the maximum activity in the l eft ventricle . Using the data from ten patients with a total of 20 exams (10 rest, 10 stress) , o ut of which 7 exams (35%) contained more than a 5% difference in at least one of the five regions within the polar plots generated from reconstructions using th e largest and smallest user shifts , only 1 exam (5%) contained more than a 10% difference i n one region ( which had an 11% difference). I n this exam , the minimum user shift did not place all of the PET activity within the cardiac tissue in the CTAC, where v isual v erification demonstrated that this user u nder - corrected the misregistration as shown in Fig. 5.5 and Fig. 5.6 . This is an example of extreme user shift variation, which resulted in the largest regional difference between the manual shifts . The first user recorded a 3.9 mm right shift, a 1.6 mm posterior 102 shift, and a 2.3 mm inferior shift. The second user recorded an 11 mm right shift, a 1.8 mm anterior shift, and a 3.0 mm inferior shift. (a) (b) Figure 5.5: Difference in the shift values in t he axial plane for the same patient by two users . (a) (b) Figure 5.6: Difference in the shift values in the coronal plane for the same patient by two users. 5.3.3 Comparison of Un shifted and S hifted Image Reconstruction s Shifted standard CTAC r econstructions were compared to the original unshifted reconstructions for the t en patients listed in Table 5.2 i n order to quantify the impact of the registration. For these misaligned exams, the reconstruction based on the maximum user shift was compared t o the original CTAC alignment. The maximum regional difference was 37%, and the maximum regional difference per exam averaged across all 103 misaligned exams was 20%. The primary region of artifact/polar plot diffe rence was the lateral/anterior boundary of t he heart. 5.4 Automated vs. Manual Registration To compare the manual ly shift ed values, PET data and the standard CTAC data were automatically aligned using our automatic registration algorithm . This algorithm registered the data by first segmenting the heart in the PET data using fuzzy c - mean clustering. The cardiac region in the CT image is then estimated based on the seeded region - growing approach . The edge information from the PET clustered images and the CT cardiac/lung boundary is then used to find the mi nimum distance between the edges of the two modalities in a least squares sense . The automated registration process was performed on the datasets of eight patients containing 16 exams (rest and stress) . The PET and CT images were aligned using our automat ed softw are , and all of the shift values were recorded. The same datasets were aligned manually by four users , and the shift values that were assigned by each user were recorded. A detailed a nalysis was performed to extract any inconsistences in the shif t values due to the subjective assessment s of different users. The shift values obtained from these automated and manual alignment s are listed in Table 5.4 through Table 5.13. Table s 5.4 and 5. 5 show the shift values in the x, y, and z plane s for the rest and stress exam s , resp ectively. Tabl es 5.6 and 5.7 show the average of the shift values obtained by four different users for the rest and stress exam s , respectively . The average magnitude of the shift values obtained with the automatic registration softwar e, including both the rest and the stress exams, was 14.31 mm, which is greater than the average magnitude of the shift values obtained with manual 104 registration for the rest and stress exams, which was 12.45 mm . Table s 5.8 and 5.9 show t he maximum shifts a ssigned by the user s in the x, y, and z plane s for the rest and stress exam s, respectively. Table s 5.10 and 5.11 show the difference in the shift values obtained using our automated registration software and the shift values obtained by averaging the shift values from the four users. Table s 5.12 and 5.13 show the difference in the shift values obtained using the automatic registration software an d the maximum shift values from the four users. The Euclidean shift value given in each table characterizes the o verall effect of the three shift values. 105 Table 5.4: S hift values obtained using our automated software applied to the PET/CT data collected during the rest exam. Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 - 8.0 - 2.0 - 18.8 20.5 2 7.0 - 6.0 11.3 14.5 3 - 12.0 - 3.0 - 15.0 19.4 4 - 3.0 0.0 - 11.3 11.6 5 - 7.0 1.0 - 11.3 13.3 6 - 11.0 - 3.0 - 15.0 18.8 7 - 7.0 0.0 - 7.5 10.3 8 - 6.0 - 3.0 0.0 6.7 Avg. - 5.88 - 2.00 - 8.44 14.40 Table 5.5: S hift values obtained using our automated software applied to the PET/CT dat a collected during the stress exam . Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 - 5.0 4.0 - 15.0 16.3 2 25.0 - 6.0 22.5 34.2 3 - 4.0 0.0 - 11.3 11.9 4 - 3.0 2.0 - 7.5 8.3 5 - 6.0 2.0 - 7.5 9.8 6 0.0 0.0 - 15.0 15.0 7 - 4.0 - 1.0 - 11.3 12.0 8 - 5.0 0.0 - 3.8 6.3 Avg. - 0.25 0.13 - 6.09 14.22 106 Table 5.6: Average shift values obtained from four users using manual alignment applied to the PET/CT data collected during the rest exam . Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 - 7. 0 - 3.2 - 11.1 13.5 2 - 0.4 - 2.4 4.8 5.5 3 - 8.8 - 5.3 - 12.0 15.8 4 - 7.2 - 1.1 - 3.4 8.0 5 - 9.4 - 1.5 - 3.8 10.3 6 - 13.6 - 6.4 - 5.2 15.8 7 - 6.6 - 0.8 - 2.4 7.0 8 - 11.0 - 1.6 0.6 11.2 Avg. - 8.00 - 2.78 - 4.04 10.89 Table 5.7: Average shift values obtained from four users using manual alignment appli ed to the PET/CT data collected during the stress exam. Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 - 11.9 - 3.4 - 9.0 15.3 2 19.9 - 1.4 19.9 28.2 3 - 10.7 - 6.8 - 7.2 14.7 4 - 10.0 - 3.2 - 4.8 11.6 5 - 9.2 0.1 - 3.2 9.7 6 - 9 .1 - 6.7 - 7.9 13.8 7 - 7.7 0.0 - 3.4 8.4 8 - 10.5 - 0.1 0.1 10.5 Avg. - 6.15 - 2.73 - 1.92 14.01 107 Table 5.8: Maximum shift values obtained from four user s using manual alignment applied to the PET/CT data collected during the rest exam. Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 - 7.3 - 7.9 - 12.8 16.7 2 - 2.4 0 9.1 9.4 3 - 11 - 8.5 - 14 19.7 4 - 11.6 0 - 2.4 11.8 5 - 11.6 - 6.1 - 6.1 14.5 6 - 20.1 - 4.9 - 0.6 20.7 7 - 7.9 0 - 3.5 8.6 8 - 12.1 - 2.3 - 3.3 12.8 Avg. - 10.5 - 3.7 - 4.2 14.3 Table 5.9 : Maximum shift values obtained from four users using manual alignment applied to the PET/CT data collected during the stress exam. Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 - 14 - 9.7 - 7.3 18.5 2 24.8 - 1.9 20 31.9 3 - 14.9 - 8.6 - 3.5 17.6 4 - 12.2 - 4.3 - 5.5 14.1 5 - 11 - 1.8 - 3 11.5 6 - 12.1 - 7.3 - 8.2 16.3 7 - 11 0 - 1.2 11.1 8 - 11.6 0 0 11.6 Avg. - 7.75 - 4.20 - 1.09 16.58 108 Table 5.10: Difference in the shift values between the automatically registered and the average manual shifts in the rest exams. Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 1.00 1.20 7.65 7.8 2 7.45 3.55 6.40 10.4 3 3.18 2.33 2.98 4.9 4 4.18 1.08 7.90 9.0 5 2.43 2.53 7.45 8.2 6 2.55 3.38 9.85 10.7 7 0.45 0.75 5.10 5.2 8 5.05 1.43 0.63 5.3 Avg. 3.28 2.03 5.99 7.70 Table 5.11: Difference in the shift values between the automatically reg istered and the average manual shifts in the stress exams. Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 6.88 7.35 6.03 11.7 2 5.10 4.63 2.63 7.4 3 6.73 6.88 4.00 10.4 4 7.03 5.23 2.75 9.2 5 3.20 1.90 4.35 5.7 6 9.13 6.70 7.05 13.3 7 3.68 1.00 7.88 8.8 8 5.50 0.08 3.83 6.7 Avg. 5.90 4.22 4.81 9.15 109 Table 5.12: Difference in the shift values between the automatically registered and the maximum manual shifts in the rest exams. Exam X (mm) Y (mm) Z (mm) Abs. Euc (mm) 1 0.7 5.9 5.95 8.4 2 9.4 6 2.15 1 1.4 3 1.0 5.5 1 5.7 4 8.6 0 8.85 12.3 5 4.6 7.1 5.15 9.9 6 9.1 1.9 14.4 17.1 7 0.9 0 4 4.1 8 6.1 0.7 3.3 7.0 Avg. 5.05 3.39 5.60 9.49 Table 5.13: Difference in the shift values between the automatically registered and the maximum manual shifts in the stress exams. Exam X (mm) Y (mm) Z (mm) Euclidean (mm) 1 9.0 13.7 7.7 18.1 2 0.2 4.1 2.5 4.8 3 10.9 8.6 7.75 15.9 4 9.2 6.3 2 11.3 5 5.0 3.8 4.5 7.7 6 12.1 7.3 6.8 15.7 7 7.0 1 10.05 12.3 8 6.6 0 3.75 7.6 Avg. 7.50 5.60 5.63 11.68 110 6 Discuss ion The ability of positron emission tomography (PET) to depict the metabolic activity variations between healthy and affected area s of the brain has greatly improved the accuracy of detecting and staging different neurological disorders including Parkins disease, neurodegenerative disease, epilepsy , etc . [85 - 86] . However, due to the low resolution of PET scans and the lack of anatomical details, the localization of abnormalities becomes a big challenge. Some of the se details can be estimated through t he tracer uptake in various anatomical structures , but these a re not comparable to the fine details provided by other imaging techniques such as computed tomography (CT) [87 - 90]. To address this , the fusion of functional and anatomical imaging is used for many clini cal applications . A problem that is inherent to hybrid PE T/CT imaging of the brain is patient motion during d ata acquisition . The patients suffering from neurological disorders are often incapable of f ollowing verbal instructions and are more lik ely to shift the position of their head during the exam. Head restraints are used is some cases , but these are not sufficient to eliminate the head motion completely. In cardiac studies, even if other physical motion of the patient is constrained , physiol ogical movement of the organs during the respiratory cycle due to the motion of the diaphragm cannot be prevented. A recent study by Gould et al. (2007) at the Weatherhead PET center for preventing and reversing atherosclerosis showed that 40% of PET/CT ex ams contain a hypoperfusio n artifact that is caused by misregistration between the two modalities [5] . Misregistration has a greater effect on the anterior and anterolateral 111 segments of the PET heart, producing a significant reduction in the measured uptak e in these areas. This is due to the large difference in the attenuation parameters of cardiac and lung tissue and the fact that the anterior and lateral segments have the largest common surface with the lungs, whereas the septal and inferior walls are in contact with other soft tissue (right ventricle, liver, etc.). Thus, misalignment less frequently produces significant errors in the attenuation factors for these other areas. One approach to address the PET/CT misalignment problem is to obtain multiple CT scans. The PET images are matched with the CT images, and the CT with the smallest registration error is selected for PET attenuation correction. T his method does not guarantee c onsistent alignment between PET and CT images , and in some ca ses, none of the CT scans align with the PET data, which introduces metabolic or perfusion artifacts into the reconstructed PET images. Another possible approach is to reduce the temporal resolution of the CT to match that of the PET examination. This is achieved with an ultraslow CT acquisition or a respiration - averaged CT. These approaches can reduce the breathing - induced misalignment at the expense of increased radiation dose for the patient or longer acquisition times. However, misalignment resulting from other source s, e. g., patient motion or changes in the heart location due to pharmacologic stress agents, remains uncorrected with this approach. The inconsistent alignment between the PET and CT data reinforces the need for image registration software that can automat ically align the two modalities and generate a CTAC that completely overlaps with the PET data. In the brain studies, the registration of the PET and CT data is a linear procedure that is limited only t o translation and rotation. When linear transformation s are applied to the misaligned CT , the size and shape of the 112 brain remains unchanged , which makes the alignment process much easier. Th e image registration in cardiac PET/CT e xams is more complex, where non l inear transformations are needed when the heart contracts , expands , and rotates nonlinearly. In such case s, data warpi ng or deformation algorithms can also be required for accurate alignment. PET/CT brain registration utilize s 6 degree of freedom (DOF) linear transformations , which means that the segm ented brain geometry obtained from the CT data is translated and rotated with respect to the x, y, and z axes to correct any misalignment of the head that occur s during th e exam. These include shifts and rotations in the sagittal, coronal, and the axial pl ane s, where the rotations are with respect to the x, y, and z axes , respectively. T he results from multiple case studies indicate that most of the translational misregistration is along the x and z axes, whereas little or no misalignment occurs along the y axis. The re a son that no y - axis misalignment occur s is that , for this type of motion , the patient has to lift his or her head from the bed which , in most cases , is restricted using a restraining band on the forehead. The sourc e of rotational misregistrati on is that the third type of rotation, where the head rotates around the y - axis (or towards the shoulders) , is rarely observed in any of the patient data . 6.1 Effects of Overc orre ction A large CTAC shift does not always result in a significant difference in th e reconstructed images [ 91 ] . In the example below , the initial CTAC demonstrated severe misalignment (one of the largest misalignment s in any of the studies ) , which was most likely caused by patient mot ion. The PET activity was initially aligned right and inferior o f the left ventricle 113 in the CTAC images . Since the PET heart was initially positioned over soft tissue, this provided similar attenuation corre ction to that of card iac tissue. T herefore, the artifacts were not as significant as the hypo - perfusion art ifacts created when the left ventricle activity is superimpose d over the lung in the CTAC . However, i n this example, t here was still a difference of 7% in the lateral pol ar plot region . Figures 6.1 (a) and (b ) show the misaligned PET and CT images in the axial and co ronal planes , and Figures 6.1 (c ) and (d) show the same images after alignment. Figures 6.2 (a) and (b) show the polar p lots of the PET images generated before and after alignment. Fig. 6.3 shows the difference between t he two polar plots. T he difference plot shows that , even though the error in the PET data reconstructed with the misaligned CTAC is noticeable, these are much smaller than the errors caused when the PET heart overlaps with the lung in the CT image . 114 (a) (b) (c) (d) Figure 6 .1 : PET cardiac region overlaid onto (a) the misaligned CT AC in the axial plane, (b) the misaligned CT AC in the coronal plane , (c) the aligned CT AC in the ax ial plane , and (d) the aligned CT AC in the coronal plane . 115 (a) (b ) Figure 6.2: Polar plot of the reconstructed PET data generated using the (a) misaligned CTAC and (b) the aligned CTAC. The comparison shows that attenuation artifacts were presen t in the PET data reconstructed using the misaligned CTAC. Fig ure 6.3: Polar plot of the difference between the PET data reconstructed using the misaligned CTAC and the aligned CTAC shows that even though there was a significant misalignment between t he PET and CT data, the error in the reconstructed PET data is much smaller than the errors caused when the PET heart overlaps with the lung in the CT image . 116 6.2 Heart and Lung Volume Correlation To find the diastolic phase among the ten different phases with in which the CT is gated , all of the phases are compared with respect to the number of pixels in the lungs, and the CT dataset with the smallest number of pixels within the lungs is chosen to represent the diastolic phase where the heart is the largest . Th is is because the CT is acquired in a breath - held state , so the difference in the size of the lung is caused by the change in the size of the heart. PET/CT registration results are generated with all of these phases, and the shift values are calculated for each of the datasets. The shifts required for each of these datasets is then analyzed to find the CT phase that maximally overlaps the PET image in the cardiac region . A fter a ll of the datasets are analyzed, the correlation between the changes in the hea rt volume and the corresponding changes in the lung volume during the cardiac cycle is determined. Due to the very high contrast between the lung and all of the other organs, automatic and efficient segmen ta t ion of the lung is achieved much more easily tha n automatic seg mentation of the heart . Once the lung is segmented , the volume of the lung within each cardiac phase is calculated for every patient and then is compared to the heart volume . Fig. 6.4 shows that the volume of the lung and the heart is consis tent ly correlated within different phases. For most patients , th e volume of the heart is maximized at the 70% phase , and the lung volume is minimized at this phase . The opposite holds for the 30% phase. Due to this consistent relationship between the lung volume and the heart volume , the lung segmentation results can be used to efficiently estimate the diastolic phase. Fig. 6.5 shows a scatter plot of the heart contours at the systolic phase and at the diastolic phase. The blue dots represent the contours o f the heart at systole , 117 and the green dots represent the con tours of the heart at diastole . As shown in Fig. 6.5, t he siz e of the heart is much larger in the diastolic phase. Cardiac Phases (%) Cardiac Phases (%) Figure 6.4: N ormalized volumes of the heart and lung within different cardiac phases using the values calculated from segmented CT data. 118 Figure 6.5 : Contour s of the heart in the 30% cardiac phase , which corresponds to systole, and the 7 0 % cardiac p hase , which corresponds to diastole . The systolic cardiac volume shown in blue is significantly smaller than the diastolic cardiac volume shown in green. 6.3 Attenuation - Corrected and Non Attenuation - Corrected Data Automatic segmentation and registration is applied to the attenuation corrected (AC) PET images as opposed to the non - attenuation corrected (NAC) PET images which are less homogeneous due to differential attenuation of the brain region and due to the higher noise factor. The problem, however, with the AC PET data is the inherent hypo - metabolism artifact that can be present in the attenuation correction with a misregistered CTAC. To ensure the robustness of the b rain segmentation results and to uncover any bias present in the segmented brain boundary due to a possible hypo - metabolized b rain region, both the AC and the NAC PET data are segmented in all patients with hypo - 119 metabolic artifacts. The results show that a consistent brain boundary is generated for both the NAC and the AC PET data . The pixel intensities for the hypo - metabolized r egion, which are lower than those for the normal brain region, still have sufficient contrast with the air and bone intensities to ens ure correct boundary detection f or the brain. The segmented brain contours using the hypo - metabolized PET images show no b ias due to the inherent hypo - metabolic artifact. For all of the patients with misregistered PET/CT images , the reconstructed PET images using the registered CTACs are again processed with the automated registration software , and the two images consistently align correctly. 6.4 Hyper - perfusion Artifact In one exam, the PET data showed abnormally high blood perfusion in the left ventricle, which was caused by calcification in the heart. The CT attenuation map used for PET image reconstruction also showed calcific ation in the heart . When this occurs, the attenuation parameter for bone is assigned to this region, resulting in erroneous overcorrection. Fig. 6.6 (a) show s a CT image in the axial plane in which the bright region with in the left ventricle represents the calcification. Fig. 6.6 (b) show s the corresponding PET slice with artifactual hyperperfusion after reconstruction. 120 (a) (b) Figure 6.6 : Calcification in the heart (a) is observed in th e CT sli ce in the axial plane, and (b) causes a hyperperfusion artifact in the reconstructed PET slice. 121 7 Summary and Future Work The work of this Ph.D. thesis is summarized below along with a list of improvements that are expected to further enhance PE T/CT image reconstruction . 7.1 Summary Single gantry hybrid PET/CT imaging system s provide noninvasive assessment of functional information as well as structural detail. The main advantage of PET/CT imaging over the use of PET transmission attenuation correcti on maps for image reconstruction is the shorter overall acquisition time resulting in greater patient throughput. In a traditional standalone PET system, the time required to obtain the transmission map is about 30 - 40% of the total scan time, which is on t he order of several minutes. In contrast, CT scans for attenuation correction are acquired in a few seconds. Another advantage of CT based attenuation correction is the lower noise level in CT images than in traditional transmission scans, resulting in rec onstructed PET images with higher signal to noise ratios. A common pitfall of PET/CT imaging is the potential mismatch between the position of the heart in the PET and the CT data. One of the reasons for this mismatch is patient motion. The PET images are acquired several minutes after the CT scan, providing the opportunity for significant patient motion. Even if the patient manages to stay still during the entire image acquisition process, physiologic respiratory motion can cause misregistration between t he PET and the CT data. This misregistration can significantly affect the reconstructed PET image by projecting erroneous CT attenuation parameters 122 onto the PET data , thereby creating false areas of low or high tracer uptake that can increase the chances o f diagnostic misinterpretation. One approach to address the PET/CT image misalignment problem is to obtain multiple CT scans, but this method does not guarantee accurate alignment of PET images with any of the acquired CTACs. Also, multiple CT acquisition s cause unnecessary radiation exposure in the patient. Another approach is to manually align all of the PE T/CT exams, which is quite time - consuming and can vary depending on the subjective judgement of the operator. A better solution to this problem is pr ovided by a software program that automatically r egisters the two modalities to eliminate the attenuation artifacts from the reconstructed PET data . This software - based method aligns the PET and CT data by calculating the distance between the cardiac bound aries of the PET and CT data . An aligned CT attenuation correction (CTAC) map is generated using the shift values obtained from PET/CT image registration. The PET images are then reconstru cted using the shifted CT data . T ests on PET/CT images from several pat ients were performed to ensure the consistency of the automated registration software in aligning the two modalities and eliminating the attenuation artifacts . Results show that only one CT scan is required for each patient and that the registered CT at tenuation map successfully generates artifact - free PET images. By acquiring only one CT scan for PET data reconstruction, the radiation dose delivered to the patient is minimized, and an efficient clinical workflow is achieved . 123 7.2 Contributions This thesis ma kes the following contributions to PET/CT imaging: - A utomated software was created for the registration of volumetric PET/CT data in order to remove artifactual attenuation defects from reconstructed PET images . The software ensures a minimal radiation dose for the patients by eliminating the need for multiple CT acquisitions. - Multiple respiratory phases were evaluated for the CT images to determine the phase which consistently gives better alignment than the other phases. - The software was vali dated for all the respiratory phases with a utomated respiratory motion compensation of the heart to accurately align the PET and CT cardiac geometries. - T he optimal cardiac phase of the CT images that maximally overlap with the cardiac region in the PET images was estimated . To ensure that the cardiac region in the PET images completely overlaps the cardiac region in the CT images , the CT images must be acquired in the diastolic phase. Analysis shows that the 70% phase corresponds to diastole and is optim al for the reconstruction of PET data. - GE Discovery STE compatible DICOM images of the aligned CTAC were generated with our registration software to reconstruct PET images for efficient clinical workflow and minimum manual intervention. 124 - N on - attenuat ion corrected (NAC) PET data and the pre - attenuation corrected (AC) PET data were analyzed to identify any inherent bias in the segmentation process. - T he automated image segmentation/ registration was validated against the manual alignment performed ind ependently by multiple technicians on the same datasets in a comprehensive study . - A m ulti - slice to po lar map transformation of the left ventricle data was performed to give a better representation of the condition of the heart. 7.3 Future Work Some of the a spects that can be explored in the future are discussed below . 7.3.1 Dual Gating for PET Data Acquisition Data acquisition for the PET scans take s several minutes wherein the readings are averaged over multiple cardiac and respiratory cycles , which causes blurr ing of the image data resulting in reduced spatial resolution . To minimize this problem , simultaneous respiratory and cardiac gating should be performed. List - mode data should be associated with the triggers from respiratory and cardiac cycles and then re constructed after compensating for the two types of motions. During a cardiac cycle, there is a significant change in size as the heart goes from systole to diastole , and during the respiratory motion of the patient , the heart can be displace d up to 2 cm d ue to the movement of the diaphragm . This translation and deformation of the heart results in blurring of the data due to the overlapping of different parts of the heart acquired at different times. The blurring of the data restricts the use of PET/CT imag es for small 125 defects. If all of the transformations are compensated before averaging the data points, then sharper images can be acquired in which minu te defects can also be detected and analyzed. 7.3.2 Left Ventricle Deformation Correction In addition to the tr anslation of the heart during the respiratory cycle and the change in the size of the heart during the cardiac cycle from systole to diastole, the heart walls also go through a non - linear warping [92], as shown in Fig. 7.1. Due to this warping , correspondi ng point s on the surface of the heart wall appear at significantly different location s in the three dimensional image space. The uncompensated averaging of the PET data produces an erroneous averaged value for each location in the heart. In order to averag e the exact physical points of the heart over time, compensation for the deformation that the heart undergoes in a cardiac cycle is also needed . Depending on the accompanying ECG signal, the transformation model can be applied to the pixels of the cardiac region to correlate all of the corresponding points at different acquisition times. After compensating for the deformation, the volumetric data can be averaged together in order to obtain the correct intensity values at all points in the heart. Fig. 7.1 sh ows the left ventricle at two different phased of the cardiac cycle in which the corresponding points of the heart do not overlap with each other . 126 (a) (b) Figure 7.1: Transformation of the left ventricle during the cardiac beat cycle where (a) shows two point on the myocardial wall, and (b) shows that the same points do not overlap when the cardiac wall is warped. 7.3.3 Estimation of Myocardial Blood Perfusion Noninvasive measurement s of myocardial blood flow are diffic ult to accomplish be cause of the low spatial resolution of currently available systems [93 ] . The quantification of blood flow is important in estimating the condition of the heart. If the flow t o the heart is insufficient, this can result in m yocardial ischemia , which in turn can l ead to infarction. With a contrast agent, tracer kinetic models can be used to estimate the regional blood flow, but this can only be achieved with high temporal resolution. Due to the low spatial resolution of the PET scanners, the physiological mot ion of the heart during the cardiac and respiratory cycles significantly degrades the quality of the image which limits the accuracy of the quantitative studies for myocardial blood perfusion. If the deformations of the heart are accurately compensated as mentioned in the previous sections, the kinetic models can be helpful in the estimation of the blood flow. A graphical user interface f or 127 viewing and analyzing PET data in different planes and in polar map form i s shown in Fig. 7.2. Figure 7.2 : Graphical interface for viewing cardiac PET data and for generating and analyz ing the pol a r maps . Fig. 7.3 shows the polar maps generated using the PET data acquired at different times during the dynamic study. The intensity values at the corresponding locations i n all of the polar maps can be used in a kinetic model to estimate tissue parameter s . 128 Fig ure 7.3 : Polar maps of the cardiac data acquired at different times. 129 7.4 Papers Written 1. Compe nsation in PET/CT for Accurate Reconstruction of PET Myocardial Perfusion 2008. 2. K. L. Berger, J. L. Seamans, K. Khurshid, E. Philps, R. J. McGough "CTAC Misregistration in PET/CT Cardiac Imaging: Correction with a Dedicated CTAC/PET Alignment Visualization Application, an Automated Registration Algorithm, and ECG - Gated CTAC", American Society of Nuclear Cardiology, Journal of Nuclear Cardiology, 2007, Vol. 14 Issue 4, pS105. 3. D. J . VanderLaan, K. Khurshid , J. J. Ireland, F. J. Krassel, R. J. 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