Analysis of gated myocardial perfusion SPECT images using computational image registration techniques

ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES RAQUEL DA SILVA ALVES DISSERTAÇÃO DE MESTRADO APRESENTADA À FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO EM ÁREA CIENTÍFICA M 2014 ii iii ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES Dissertation submitted in fulfillment of the requirements of “Dissertation” Course of Master Degree in Biomedical Engineering Raquel da Silva Alves Degree in Biomedical Engineering from the University of Trás-os-Montes and Alto Douro (2012) Monograph prepared under the supervision of: Professor Doutor João Manuel R. S. Tavares (supervisor) Department of Mechanical Engineering Faculdade de Engenharia da Universidade do Porto, Portugal Professor Doutor Durval Campos Costa (co-supervisor) Nuclear Medicine – Radiopharmacology Champalimaud Centre for the Unknown Champalimaud Foundation iv v Abstract Modern medicine has been widely using imaging as a fundamental tool to aid in diagnosis procedures, monitoring the evolution of pathologies and the planning of treatments and surgeries. Myocardial perfusion is commonly studied through the evaluation of the left ventricular function using stress-rest gated myocardial perfusion single photon emission computed tomography (SPECT). SPECT provides a suitable identification of the myocardial region, facilitating both the identification and localization of perfusion abnormalities. A suitable performance of semior full automated methods for intraor inter-modality registration and automated methods for computer quantification of LV functional abnormalities can minimize interand intra-observer variability and increase the reproducibility, which have an important role in risk stratification and selection of the best treatment strategy. Here, computational techniques of medical image analysis, mainly of image registration, are integrated in a computational solution to automatically compute a set of features from myocardial perfusion SPECT images and use them to statistical analysis and classification of patient exams as from a healthy patient or with an associated disease. The image registration algorithms used, including the transformation, similarity measure, optimization and interpolation algorithms, will be described and discussed, as well as the computational processing, analysis and classification techniques employed. Experimental results will be presented and discussed. Keywords: Image registration, image processing and analysis, image segmentation, image classification, myocardial perfusion SPECT images. vi vii Resumo A medicina moderna tem vindo a utilizar a imagiologia como uma ferramenta fundamental no apoio aos procedimentos de diagnóstico, monitorização da evolução de patologias e planeamento de tratamentos e cirurgias. A perfusão do miocárdio é comummente estudada através da avaliação da função do ventrículo esquerdo (VE) usando a tomografia computorizada por emissão de um único fotão (SPECT) com acoplamento ao sinal electrocardiográfico em estado de esforço físico e de repouso. A SPECT permite identificar a região do miocárdio, facilitando a identificação e localização de anormalidades de perfusão. Uma performance adequada de métodos semi ou completamente automáticos para o alinhamento intere intra-modalidades, e também de métodos automatizados para a quantificação computorizada das anormalidaes funcionais do VE, podem minimizar a variabilidade intrae interobservador, aumentando a reprodutibilidade que é fundamental para a estratificação do erro e selecção da melhor estratégia de tratamento. Nesta dissertação, técnicas computacionais de análise de imagem médica, principalmente de alinhamento de imagem, são integradas numa solução computacional que automaticamente calcula um conjunto de características de imagens SPECT de perfusão do miocárdio. Estas são utilizadas para análise estatística e classificação dos pacientes como estando associados a pacientes saudáveis ou com doenças cardíacas associadas. Palavra-chave: Alinhamento de imagem, processamento e análise de imagem, segmentação de imagem, classificação de imagem, imagens SPECT de perfusão do miocárdio. viii ix Agradecimentos Ao orientador Prof. Dr. João Manuel R.S. Tavares, pelo apoio e orientação prestados ao longo deste mestrado, tanto ao nível da dissertação como na publicação de comunicações científicas relacionadas. Ao co-orientador Prof. Dr. Durval Campos Costa, da Fundação Champalimaud, pela sua disponibilidade para orientação da presente dissertação e pela oportunidade de trabalhar com um profissional da sua excelência. Ao Diogo Faria, do Hospital dos Lusíadas Porto, pela disponibilidade e apoio técnico constantes. Sem o seu contributo, esta dissertação não seria possível. À Universidade de Trás-os-Montes e Alto Douro que em muito contribuiu para a minha formação pessoal e profissional em Engenharia Biomédica, nomeadamente aos professores que me orientaram durante todo o meu percurso académico. A Vila Real, uma cidade que deixa saudade, pela sua beleza, pelo espírito académico, pelas pessoas com que me permitiu cruzar, pelas histórias que guardo na memória, pelos companheiros e afilhados da praxe académica e pelos amigos que ficaram para a vida. À Faculdade de Engenharia da Universidade do Porto, que com a sua excelência, levou ao amadurecimento exponencial dos meus conhecimentos em Engenharia Biomédica. À Banda Musical de Gondomar, e ao maestro Luís Carvalhoso, que compreendeu a disponibilidade reduzida para as actividades relacionadas durante este ano lectivo, devido ao estatuto trabalhadora-estudante. xvi xvii ABBREVIATIONS AND SYMBOLS List of abbreviations (sorted alphabetically) AIR Automated Image Registration AMIDE Amide is a Medical Image Data Examiner ANTs Advance Normalization Tools ART Algebraic Reconstruction Techniques CC Correlation Coefficient CT Computerized Tomography ERNA Equilibrium Gated Radionuclide Angiography FFD Free Form Deformation FIRE Functional Image Registration FLE Fiducial Localization Error FOV Field-Of-View FPRNA First-Pass Radionuclide Angiography FRE Fiducial Registration Error GLIRT Groupwise and Longitudinal Image Registration Toolbox GSPECT Gated Single Photon Emission Computed Tomography ITK Insight Toolkit LOP Left Posterior Oblique LV Left Ventricle LVEF Left Ventricle Ejection Fraction MAbs Monoclonal Antibodies MAP Maximum A Posteriori MART Multiplicative Algebraic Reconstruction Techniques MI Mutual Information MIRT Matlab Image Registration Toolkit MLEM Maximum-Likelihood Expectation Maximization MRI Magnetic Resonance Imaging OpenGL Open Graphics Library xviii OSEM Ordered Subset Expectation Maximization OSL One Step Late PET Positron Emission Tomography PIU Partitioned Intensity Uniformity PTM Photo-Multiplier Tubes RC Residual Complexity RMIPs Radiolabeled molecular imaging probes RIU Ratio Image Uniformity RMS Root Mean Square SAD Sum of Absolute Differences SD Standard Deviation SPM Statistical Parametric Mapping SPECT Single Photon Emission Computed Tomography SSD Sum of Squared Intensity Differences TPS Thin-Plate Splines TPS-RMS Thin-Plate Spline Robust Point Matching TRE Target Registration Error VIR Variance of Intensity Ratios VTK Visualization Toolkit WBR Wide Beam Reconstruction WLS-CG Weighted Least-Squares Conjugate Gradient List of symbols 𝛾 Gamma ray ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 1 Chapter 1 Introduction 1.1. Motivation & Goals Modern medicine has been widely using imaging as a fundamental tool to aid in diagnosis procedures, monitoring the development of disease and planning treatment or even surgeries. Thus, it became a key element to support medical decision making through non-invasive procedures. In the last years, deep researches and developments have been increasing lead to a higher number of information types that can be acquired from such diagnostic tool. Image registration computer techniques enable the integration of different medical image modalities and the easier detection of changes between images acquired from different points of view, different acquisition times or even with subject atlas to attain prior anatomic or functional information. It stresses changes in size, shape or image intensity over time, and relates both preoperative image and surgical plans to the physical reality of patients during intervention and aligns patient’s anatomy to a standardized atlas. Techniques of image registration aim the establishment of spatial correspondence with the goal of find the optimal transformation that best aligns the structures of interest in the input images. The minimization of an error measure, or of a cost function, is the goal of these techniques. Additionally, an optimization algorithm is needed to find the most suitable transformation, and an interpolator is employed to resample the features into the new registered space. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 2 The application of image registration techniques in nuclear medicine includes correlative image interpretation, attenuation correction, scatter correction, correction for limited resolution and improvement of the reconstruction accuracy in emission tomography. These techniques also have been used in the co-registration of serial functional studies, for the transformation to standard spaces for their comparison with both normal studies and data from other modalities, in conformal radiotherapy treatment planning and functionally guided procedures. Besides, have been improving the interpretation of several functional studies based on static images, including brain, breast, chest, liver, kidneys and colon images, or on the motion analysis as in cardiac and lung studies. Myocardial perfusion is commonly studied through the evaluation of the left ventricular function using stress-rest gated myocardial perfusion single photon emission computed tomography (SPECT). SPECT provides a suitable identification of the myocardial region, facilitating both the localization and definition of perfusion abnormalities [2]. The automated computer quantification of LV functional abnormalities can minimize interand intra-observer variability and increase the reproducibility, which have an important role in risk stratification and selection of the best treatment strategy. With such computational solution, the prevalence and clinical predictors of both myocardial ischemia and infarct in suspicious patients can be easier assessed. Motivated by the potentialities of the application of computational techniques on stress-rest gated myocardial perfusion SPECT images referred above and their application, the goal of this dissertation consists of developing a computational solution to automatically compute a set of features from myocardial perfusion SPECT images and use them to statistical analysis and classification of patient’s exams as from a healthy patient or with an associated disease. 1.2. Organization This dissertation is divided into the following chapters: 2. Gated Myocardial Perfusion SPECT Images The second chapter describes SPECT imaging modality, describing the radiotracers commonly used, detectors and related image reconstruction algorithms. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 3 Its main advantages and problems are referred, as well as clinical applications. Therefore, general principles of myocardial perfusion gated SPECT are exposed. 3. Medical Image Registration In this chapter, medical image registration is presented through a state-ofthe-art by the study and description of its methodologies and respective classification, as well as the main types of transformations, similarity measures, optimization and interpolation techniques involved in the process. 4. Image processing, segmentation and quantitative analysis Computational image techniques employed in this experimental implementation are described. 5. Experimental implementation The computational solution developed to automatically segment, analyze and classify the images as from subjects with myocardial perfusion associated diseases or not is described. Experimental results will be also presented and discussed. 6. Final considerations Final conclusions and future works will be described in this last chapter. 1.3. Contributions This dissertation presents a deep study and bibliographic revision of scientific literature in medical image registration and its applications on nuclear medicine images, specifically in gated myocardial perfusion SPECT images. The main contribution is the development of a template myocardial perfusion SPECT image and its coronary artery mapping, enabling the computation of mean geometric dimensions in healthy patients. Thus, image classification is reached through registration of the patient’s images under study with the template myocardial perfusion SPECT and comparison of related geometric dimensions. 4 ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 5 Chapter 2 Gated Myocardial Perfusion SPECT Images Nuclear image modalities have been widely used in healthcare diagnostic since it provides a physiological diagnose through the use of radiotracers to map metabolism and fluid flow on tissues or organs. Unlike other imaging techniques, emission tomography modalities assess both the perfusion and metabolic activity, even if there are no changes from the structural point of view. It is commonly used as a diagnose complement in oncology, cardiology and neuropsychiatric disorders. The enhancement of digital medical image acquisition and analysis, such as higher spatial and temporal resolutions, is actually the hot topic of medical imaging modalities. However, image analysis cannot be properly achieved without the development or better integration of different registration methods. They enable the integration of different medical image modalities, such as Positron Emission Tomography (PET), Single Photon Emission Computed Tomography (SPECT), Computerized Tomography (CT) and Magnetic Resonance Imaging (MRI), through the detection of differences between images acquired from different points of view, different time acquisition or even different subject atlas, to obtain anatomic and functional information that reflects completely the condition of the patient, providing a more complete information for supporting medical diagnosis. The combined evaluation of myocardial perfusion and left ventricular function within a single study is carried out through electrocardiographically gated myocardial perfusion SPECT (GSPECT). This technique has been improving through ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 6 image processing and quantification, since it enhances diagnostic and prognostic capability of myocardial perfusion imaging. Furthermore, computation image techniques improve incremental information over the perfusion data and enables myocardial viability assessment and sequential follow-up after therapy. In this chapter, SPECT imaging modality will be described, namely the radiotracers employed, detectors, image data acquisition, image reconstruction and algorithms in 2D and 3D, such as the common sources of degradation factors that minimize the quality of the images acquired and its corrections. Hybrid systems with molecular modalities commercially available and their applications are also reviewed. Its application as GSPECT is explored, namely general principles, clinical protocols and image analysis currently employed. 2.1. Single Photon Emission Computed Tomography Single photon emission computed tomography is a nuclear image modality that uses radioactive tracers, to measure and evaluate both the perfusion and metabolic processes of the individual or object under study. SPECT studies are based on electronic detection of photons, by an Anger gamma camera, administered by intravenous injection into the human body, generating three-dimensional images of the radiopharmaceutical distribution [1]. The development of 3-D algorithms was fundamental to the evolution of SPECT till nowadays. Without improvements of the Anger camera with a rotating collimator attachment and the optimization of reconstruction algorithms or interactive methods, it would not be possible to improve the low contrast characteristic of the blurred SPECT images. High-speed digital computer systems for acquisition and display of dynamic processes in the body such as the development of high-speed dynamic radionuclides, dualand triple-camera contributed to an efficient molecular imaging modality. SPECT uses time as an additional coordinate, by collecting different information as a function of time and translating this into spatial information [2]. Accordingly, it is a valuable diagnostic imaging modality [3]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 7 2.1.1. Radiotracers Respecting single photon emitting radiopharmaceuticals, it must be considered the wide availability of the radioligands as a relative ease of labeling, which is based on the consumption of oxygen. Thus, SPECT has the ability of detecting and monitoring biological and pathophysiological processes, using radiolabeled peptides and drugs [4]. The radiotracers commonly used can be classified into the following groups:  Radiolabeled molecular imaging probes (RMIPs) are highly specific radiolabeled. They allow visualization, characterization and measurement of biological processes in living systems, but must be design and chosen depending on the organ of study. Furthermore, they are classified based on their utility and nature of application, resulting in radiolabeled drug substance, radioligands [5], pathway marker and biomarkers.  Peptides and proteins enable finding radiolabeled monoclonal antibodies (MAbs). Their specifically binding forms an antigen-antibody complex, 99mTc-labeled monoclonal antibodies, sulesomab, annexin V and radiolabeled peptides.  Hypoxia imaging and cell labeling are also used, but in fewer applications [6]. Table 2.1. synthetizes the main radionuclides employed in SPECT studies and their most relevant characteristics. Table 2.1 Commonly used single photon emitting radionuclides (adapted from [6]). Radionuclide Half-life Energy Mode of decay Tc-99m 6.92h 142keV Isometric Transition (100%) I-131 8.03 days 364keV Beta-minus (100%) I-123 13.22h 159keV Electron Capture (100%) In-111 2.80days 171,245keV Electron Capture (100%) These radiopharmaceuticals contain long-lived radioisotopes emitting gamma rays that decay through an isometric transition, i.e. a nuclear de-excitation resulting ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 14 coronary artery calcium, evaluating the patency of vascular and coronary arteries and assessing myocardial perfusion, such as viability in one clinical setting, are some of the multiple applications where SPECT/CT has been applied, but it is necessary to become more available in the market, requiring lower costs [16]. In the last few years, integrated SPECT/CT systems have been widely used but MRI presents specific advantages compared with CT, such as lack of ionizing radiation, high soft-tissue contrast and sensitivity to tissue alterations evidenced by specific imaging sequences. However, using SPECT followed by MRI in clinical applications is a complicated task [26], once it requires transferring the patient to another system table and inherently separated dual-modality scans, followed by image fusion. Then, there are potential sources of misalignment due to uncontrolled movements and displacements of tissues and organs. Multiple anesthesia sessions are needed when SPECT and MRI devices are located in separate places, involving higher risks to the patient due to different biologic responses to anesthesia. Attempting to compensate these problems, there are studies using SPECT followed by low spatial resolution MRI and also SPECT/MRI performed at very high magnetic fields to achieve high anatomic resolution, benefiting from a higher signalto-noise ratio but it leads to field susceptibility artifacts and prevents closer proximity of SPECT scanner [27]. Hence, it is needed to minimize technical limitations of SPECT/MRI dual imaging, such as enhance registration methods [28]. Prototypes are being constructed to allow the minimization of all these problems, for applying dual modalities in clinical application, besides the many applications in preclinical applications [29–31]. Wherefore, integrated SPECT systems enable a direct correlation of anatomic and functional information resulting in a better definition and localization of scintigraphic findings [32]. 2.1.7. Preand Clinical Applications Preclinical models are valuable SPECT applications [33–35], having a great scope for noninvasively studies on dynamic biological processes at molecular and cellular levels. Through the assess of biological effects of drug candidates and the capability of following the development of certain diseases, molecular imaging plays an important role in the implementation of relevant animal therapeutic models in ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 15 vitro, such as cardiovascular imaging, imaging stem cells, oncologic applications [36, 37], neuroimaging applications [38–45] and drug discovery, using small-animal imaging [30, 31, 46, 47]. The preclinical application in SPECT leads to consequent applications in clinical cases, usually the same areas as PET. There are several reported cases study is scientific literature [48–50]. In oncology, it permits the detection of tumors at an early stage, since it is capable of detecting and analyzing the development state of cancer [4, 36, 51–53]. In cardiology, it allows the assessment of myocardial viability in coronary patients, allowing a more accurate selection of patients for revascularization procedures [54, 55], through the evaluation of myocardial perfusion [56–61]. In neurological and psychiatric disorders, SPECT has an important role in the study of Parkinson's disease [57–64], Alzheimer [39, 70–73], epilepsy [74], brain dementia [71] and movement disorders [69, 75–77]. Given the relevance of myocardial perfusion SPECT studies in this dissertation, general principles are next exposed, concerning radiotracers, image acquisition, image analysis and several diagnosis applications. 2.2. Myocardial Perfusion SPECT Study The combined evaluation of myocardial perfusion and left ventricular function within a single study is carried out through electrocardiographically GSPECT, since it allows the quantification of degree and extent of the LV functional abnormalities [78]. However, it is not suitable for accurate RV function measurement because it is not properly visualized on the perfusion images. This technique enables the quantitative or semi-quantitative assessment of the LV function simultaneously with the evaluation of the LV perfusion, which aid in the diagnosis, assessment of the risk and prognosis, determination of the myocardial viability and evaluation of the functional recovery after the revascularization procedure in patients with known or suspected coronary information over the perfusion data [79]. Similarly to SPECT clinical protocols exposed above, GSPECT studies require the injection of a perfusion tracer that is taken up by the myocardium. Delineation of the epicardial and endocardial edges on the perfusion image provides the definition of the LV myocardium and LV cavity [80]. LV function is based on the ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 16 quantitation of the changes in the LV volume, excursion of the endocardium and brightening of the myocardium from the end-diastolic image to the end-systolic image. Besides there are more 𝛾-camera imaging techniques available to measure the ventricular function, namely, first-pass radionuclide angiography (FPRNA) and equilibrium gated radionuclide angiography (ERNA), several factors contributed to the consistent growth of GSPECT popularity. It is simple and provides functional status information of a hypoperfused or normally perfused area. 90mTc-labeled perfusion tracers present favorable kinetics and consequently flexible acquisition protocols. Acquisition and processing time have shortened significantly due to continued improvements of multidetector 𝛾-cameras. Computers and automation of computation image techniques has made SPECT a simple, practical and user friendly technique in clinical settings [81]. 2.2.1. General principles A 𝛾-camera records the photons at multiple projection angles around the subject along 180º or 360º degrees. At each of the projection angles, one static image is acquired during an ungated image acquisition. Several dynamic images spanning the length of the cardiac cycle are acquired at equal intervals during ECG gated acquisition. This principle is illustrated in Figure 2.3. The number of frames can vary. An increased number of frames provides better temporal resolution, but each frame requires shorter duration and consequently the acquisition has to be prolonged to collect adequate counts. A proper quality GSPECT study can only be achieved with an adequate count density, which is reached through gated data acquisition over many cardiac cycles. However, they may have different duration causing mix of counts from adjacent frames, known as temporal blurring, and compromise the quality of the study. Thereby, a range of acceptable beats or acceptance window, known as tolerance, is defined; it is expressed as the percentage of the mean R-R interval. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 17 Figure 2.3. Principle of ECG-gated acquisition. Each cardiac cycle is represented by the R-R interval, divided into 8 frames of equal duration (A). Over multiple cardiac cycles, image data from each frame are acquired (B). Each data set represents a specific phase of cardiac cycle, which provides a volume curve representing endocardial volume for each of 8 frames (C). ED:end-diastole; ES: end-systole [79]. 2.2.2. Radiotracers and clinical protocols Usually, the radiotracers administered are 99mTc-sestamibi and 99mTctetrofosmin, since they have a short half-life without associated increase in the radiation burden and allow a higher dose results, with better count statistics in the images. Consequently, there are associated with lower statistical error and better image quality [82]. The clinical protocols employed can be a same-day or separate-day protocol, both illustrated in Fig. 2.4. Usually, stress study is gated as part of a low-dose rest/high-dose stress 99mTc or a rest 201TI/stress 99mTc sequence [83]. Figure 2.4. Myocardial perfusion imaging can be gated either using stress-rest (A) or rest-stress sequence(B), with 99mTc [79]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 18 The perfusion pattern reflects the myocardial distribution of the tracer at the time of injection, representing the LV function at the time of acquisition. Depending on the health condition of the patient, post-stress gated images represent stress perfusion and rest function in healthy patient or patients with previous myocardial infarction, and a reduced function during the post-stress acquisition compared with the resting basal function in patients with severe ischemia. The standard GSPECT acquisition is generally completed within 20-30minutes. For viability assessment, the protocols consist of to inject the tracer at rest and gated acquisition is performed during infusion of an inotropic agent [79]. Patients with severe arrhythmia, such as atrial fibrillation, frequent premature ectopic beats and heart block should not perform GSPECT studies, i.e. patients whose heartbeat can be affected. 2.2.3. Image acquisition and reconstruction Image acquisition is similar to a standard perfusion SPECT acquisition, but it is increased by the use of a 3-lead ECG that allows the mechanism for gating, providing the R wave. Its detection actives the gating device, that sends a signal to the acquisition computer, starting the acquisition. The frames are summed together, reconstructed and displayed in standard vertical long-axis, horizontal long-axis and short axis slices for perfusion analysis (see Fig. 2.5.). However, functional analysis requires raw data to be reconstructed frame by frame. Before reconstruction, it is fundamental to check raw projection data for potential sources of error and artifacts, since they propagate and compromise the accuracy of the measurements. 2.2.4. Image analysis The definition of the normal limits and criteria for abnormalities are crucial for optimal interpretation [84], since visual analysis requires the reader to be familiar with the pattern of the normal LV contraction in different segments of the LV. An atlas is available in scientific literature, providing the reader with both image recognition and understanding of the basis for myocardial perfusion SPECT images interpretation [85]. Furthermore, the proper delineation of endocardial contour provides higher accuracy, but the edge detection is often inaccurate in patient with severe perfusion, large aneurysmal dilation, and significant structural distortion [86]. Accuracy is also affected in patients with a smaller heart [87–89]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 19 (a) (b) The use of computer techniques provides objective quantitative assessment in interpreting these studies [85–88]. There are commercially available software packages to analyze the reconstructed gated dataset, as QGS and Emory Cardiac Toolbox, developed at Cedars-Sinai Medical Center and Emory University, respectively [79, 86]. They provide LV volumes and LVEF measurements, both displayed on a segmental, circumferential model of the LV with each segment representing a particular region of the LV. Measurement of LV diastolic indices and LV mass are currently being developed. The polar map approach is used for both representation of the patient’s LV myocardial perfusion distribution and identification of hypoperfused segments. It consists of synthetizing the 3-dimensional maximal LV count distribution onto a single 2-dimensional polar map. The count distribution at the base of the LV corresponds to the intensity at the periphery and the count at the apex to the center of the polar map. Then, the patient’s 3D LV myocardial perfusion tracer uptake ratio is compared with a statistically determined lower limit of normal LV volumes or LVEF [84], based on mean normal distribution and corresponding regional standard deviation (SD), allowing hypoperfusion detection. The extent of hypoperfusion is shown by a blackout or extent polar map, whose normalized counts of LV segments that fall below the lower limit of normal pattern are deemed to be hypoperfused [90]. Figure 2.6(a) illustrates the polar map approach. Figure 2.5. (a) From left to right, short axis, horizontal long axis and vertical long axis (adapted from [214]) and (b) correspondent myocardial perfusion SPECT slices, for perfusion analysis. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 20 The artery coronary mapping, used in visual assessment of perfusion, results from the division of the left ventricle into a variable number of segments. Usually, myocardial perfusion studies are displayed using 17 or 20 segments. The 20segmented model, which is used in the experimental implementation presented in Chapter 5, divides the myocardial perfusion region into basal, mid-cavity and apical thirds, including 2 segments for the apical cap. This approach results in a 30% contribution from the base, 30% from the mid-cavity and 40% from the apex and apical cap [91]. The assignment of segments to coronary arterial territories is directly related with the coronary artery blood supply. As illustrated by Figure 2.6(b), segments 1, 2, 3, 7, 8, 13, 14, 19 and 20 are assigned to the left anterior descending coronary artery distribution; segments 4, 9, 10, 15 and 16 are assigned to the right coronary artery; segments 5, 6, 11, 12, 17 and 18 are assigned to the left circumflex artery [91]. (a) (b) Figure 2.6. (a) Polar map representing LV normal perfusion distributions using Emory Cardiac Toolbox, for a stress sestamibi with attenuation correction. Regional tracer uptakes varies (adapted from [90]) (b) 20-segment model for apical, mid-cavity and basal locations of short axis, and long axis (from left to right) [78]. Quantitative programs have reduced subjectivity and demonstrated excellent interand intra-observer reproducibility, but repeatability on the same subject is affected by several factors, namely acquisition, data processing, quantification and physiologic variation [78, 94]. Besides, those software packages presents data that are not sufficiently intuitive to image analysis, since both statistical and visual information presented always require high professional experience from the clinical expert. 2.2.5. Clinical applications Evaluation of myocardial perfusion GSPECT studies in patients with CAD provides additional information that cannot be obtained by perfusion imaging alone. While a normal perfusion study carries an excellent prognostic value, an abnormally low LVEF in the same patient may alert the physician for other comorbidities [81]. Nonischemic and ischemic dilated cardiomyopathy can be differentiated through ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 21 combined perfusion-function analysis. A common application is to classify a fixed perfusion defect as a soft-tissue attenuation artifact or an infarct. Assessment of severity, risk stratification and prognosis [58, 95, 96], predicting future cardiac events after myocardial infarction, myocardial viability and follow-up after revascularization also benefits from GSPECT [90], due to its reproducibility and repeatability, objectiveness and extensively validation [98]. However, adequate patient selection, quality control, identification of technical limitations and application in appropriate clinical situations are important prerequisites for its optimal utilization. Digital nuclear cardiology images coupled with the tremendous advances in computer hardware and software facilitates the development of total automatic image analysis for quantification of relevant parameters and computer-assisted decision support [99], as well as multidimensional and multimodality display. 2.3. Conclusions Despite the satisfactory resolution and quality of images, research is ongoing, focused on developing better instrumentation and new software for improved performance, to reduce costs and make system more user-friendly. High technology prices and both technical and operational complexities serve as a barrier to expand the access to specialists and patients. Thus, despite the immense potential of this technology, these disadvantages require a clear definition of imaging modalities, usefulness in several fields of medicine. In the last two decades, the greatest changes have been improving spatial resolution by decreasing the crystal size and there was also a significant progress in image quality by combining 3D reconstruction algorithms and attenuation correction, to enhance temporal resolution capabilities and get a maximum artifact-free imaging modalities, such as from dual-tracers imaging and the use of specialized collimators. Co-registration with images from complementary modalities has been employed in nuclear medicine, acting as an adjunct to interpret functional nuclear medicine images, as well as offers the ability to overcome some intrinsic limitations. Multimodalities have been widely used in clinical environment and already had a valuable outcome on clinical oncology practice and cancer treatment. SPECT/CT systems applications are increasing slower due to its high cost. Although, ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 22 nuclear medicine can only benefit from such evolving integration, in which image registration plays a central role. Due to the functional diagnosis that molecular imaging provides, SPECT will maintain its applications in clinical diagnosis, assessment of response to treatment and delivery of targeted therapies, namely in nuclear cardiac applications as myocardial perfusion GSPECT studies. Automatic analysis, quantitation and proper display algorithms for the assessment of perfusion and function from myocardial perfusion SPECT have been developed and demonstrated to run successfully in the vast majority of patients [81, 94]. Here, image registration plays a central role, since it permits the comparison of single scans with a normal database and the recognition of deficiencies in myocardial perfusion [100]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 23 Chapter 3 Medical Image Registration Modern medicine has been widely using imaging as a fundamental tool to assist diagnosis procedures, monitoring the evolution of pathologies and the planning of treatments and surgeries. However, the enhancement of digital medical images and its efficient analysis cannot be completely achieved without suitable semior full automated methods for image registration [101]. Computer techniques of image registration enable the fusion of different medical image modalities and the easier detection of changes between images acquired from different points of view, at different acquisition times or even against with atlas that includes anatomical and functional information. This task of image analysis can also stress changes in size, shape or image intensity over time, relate preoperative images and surgical planned outcomes [102] with the physical world during interventions and align patients with standardized atlas [103]. The aim of image registration techniques is to find the optimal transformation that best aligns the structures of interest in the input images. For this, the techniques establish the spatial correspondence among features in the images or minimize an error measure, or of a cost function. Additionally, optimization algorithms are usually needed to find the most suitable geometrical transformations and interpolators are employed to resample the images into the registered space. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 30 The geometrical transformation model can lead to rigid or non-rigid registrations. The simplest geometrical transformation model is based on a rigid transform that considers rotations and translations, which is applied to the complete data set. Affine transform models include translations, rotations, scaling and shearing in order that the straight lines of an image are transformed to straight lines in the other image, and the parallel lines are preserved parallel [105]. The most complex transformation model implies a higher number of degrees of freedom resulting in a non-rigid transformation. Fig. 3.3 illustrates these geometrical transformations. Figure 3.3. Types of geometrical transformations: identity transformation (left); rigid transformation (center) and affine transformation (right) (adapted from [100]). Image registration algorithms based on non-rigid transformations are required, for example, when it is needed to establish the correspondence between images of one individual and an atlas [131] or computer models, and to accommodate the substantial anatomical variability across individuals [112, 113, 132, 133]. Non-rigid based registration algorithms have a higher number of degrees of freedom, when compared with rigid transformations [134, 135]. They are frequently used in image registration when the image acquisition parameters are not known [136] and usually include an initial rigid body or affine transformation that provides an initial solution for the transformation. A good pre-registration method is recommended to obtain a starting position and orientation closer to the optima nonrigid image registration solution. However, a higher number of parameters in the transformation model can introduce undesirable transformations. Then it is fundamental taking into account a regularization term [137–139]. Image registration using non-rigid transformation can be achieved using basis functions as a set of Fourier [140–143] or Wavelet basis functions [144]. Registration using splines consists of techniques based on the assumption that a set of control points maps their location in the target image into its corresponding counterpart in the source image, providing a smoothly varying displacement field ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 31 between the landmarks used. Therefore, spline-based geometrical transformations either interpolate or approximate the displacements at control points. Thin-plate splines (TPS) are based on radial basis functions and used in surface interpolation of scattered data [132, 133]. Each basis function contributes to the transformation, and each control point has a global influence on the transformation. The modeling of local deformations can be more difficult with these functions, which requires the use of free-form transformations based on locally controlled functions [145, 146]. Bsplines deform an object through the manipulation of an underlying mesh of control points generating a smooth continuous transformation. Thin-Plate Spline Robust Point Matching (TPS-RPM) algorithms has been used for non-rigid registration, showing robustness when aligning models in presence of a large amount of outliers [47]. Elastic, deformable or curved registration methods enable modeling the deformation and resampling the stretch of an elastic material, through specific transforms. Their limitations are due to the highly localized deformations that cannot be modeled due to the deformation energy from stress. There are reviews of the most promising non-linear registration strategies currently used in medical imaging, as a novel curvature based registration technique that permits a faster image registration [149], the application of deformable registration in an automated hexahedral meshing of anatomical structures [150, 151], symmetric non-rigid registration [152] and Brownian Warps, a diffeomorphism registration algorithm [153]. Fluid registration and registration using optical flow are approaches that are equivalent to the equation of motion for incompressible flow. 3.2.2. Similarity measures The characteristics of the image modalities and the nature of the misregistration must be taken into account to choose the similarity measure, as well as the type of registration, i.e. intraor inter-modality. Similarity measures can be classified into landmark, feature or intensity based metrics. Depending on the features used, some similarity metrics can be included in both classes. The similarity measure used for deformable image registration is composed of one term related to the pixel or voxel intensity or the matching between the structures in the images, and another one related to the deformation. Then, the cost function built is a trade-off between the pixel, or voxel, ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 32 intensity or matching between the structures and the constraints imposed on the deformation field. Respecting landmarks measures, the similarity measure commonly employed consists of representing the average distance between the corresponding landmarks. Similarly, surfaces or edges measures quantifies an average distance between the corresponding surfaces, or between a surface extracted in one image and its corresponding set of points in the other image [109]. The simplest similarity measure compare intensity values between images directly [100]. To register intra-subject and intra-modality images, the correlation coefficient (CC) has been an adequate similarity measure, since it involves the multiplication of the corresponding image intensities assuming a linear relationship between the intensity values. It is possible to subtract the corresponding image intensities instead of multiply them [154], allowing the adjustment of the alignment by the sum of absolute differences (SAD), as exemplified in Figure 3.4 or the smallest sum of squared intensity differences (SSD) [155]. The SSD is very sensitive to a small number of voxels that have very large intensity differences between the images to be registered. Ratio image uniformity (RIU) and variance of intensity ratios (VIR) work from a derived ratio image and are quantified as the normalized standard deviation of the voxels in the ratio image. These similarity measures are employed for intra-modality registration. Partitioned intensity uniformity (PIU) seeks to maximize the uniformity by minimizing the normalized standard deviation. It is usually used to register intermodalities images [105]. Recent image registration algorithms have been demonstrating applicable techniques based on information theory to both interand intra-modality registration. Image registration can be described as trying to maximize the amount of shared information in two images, which means that information can be used as a registration metric [156]. The joint entropy measures the amount of information existing in combined images. It has been used for rigid and non-rigid image registration [49, 50]. Mutual information can be given by the difference between the sum of entropies of the individual images at overlap and the joint entropy of the combined images [157]. Hence, it is the measure of how one image explains the other. It makes no assumptions about the functional form or relationship between image intensities [157–161]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 33 Image #1 Image #2 SAD between images #1 and #2 Figure 3.4. Application of the sum of absolute differences (SAD) to stress the differences between two images, before registration (up) and after registration (down). Before registration, or poor aligned images, the images give rise to large absolute differences, while the sum of absolute differences of well aligned images results in small differences. Changes in overlap of very low intensity regions, such as due to noise, can disproportionally contribute to artifacts that affect the registration accuracy when based on mutual information, so it is commonly used associated with normalization methods [160, 161]. 3.2.3. Optimization All the registration algorithms require an iterative approach, whose initial estimation of the transformation is gradually refined by trial and error, to calculate the similarity measure value at each iteration. So, the optimization process consists of both estimating the transformation and evaluating the similarity measure till the algorithm converges to a point when no transformation can be found with better similarity measure value [105]. Hence, the optimization algorithm computes the value of the cost function or of the similarity measure employed to relate the matching of two registered images, searching for the subsequent alignment transformations that will stop when an optimal value is achieved. It is done by searching the transformation that increase or decrease the cost function until a maximum or minimum is found, depending on the type of the cost function used. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 34 The optimization process is based on the fact that the quality of the matching of two images is balanced against some constraint. This constraint has the function of prohibiting implausible deformations and may be provided by some estimate of the energy required to physically induce the deformation [161]. One of the major difficulties is that the optimization algorithms can converge to an incorrect local optimum, because multiple optima can exist in the parameters space [162–164]. The erroneous optima can be due to interpolation artifact or local good matches between features or intensities and can be avoided by smoothing the original images. The starting position must be sufficiently close to the final position for the algorithm converge at the best answer, within its capture range [161]. To choose the solution that has the best function cost value, a multi-start optimization can be used to get the global optimal solution [61, 62]. Additionally, the images are initially registered at low resolution and then the transformation obtained is used as starting transformation in registration at the next higher resolution level [165, 166]. 3.2.4. Interpolation A process of interpolation is applied when it is intended to transform an image space into the space of another image. It is required to estimate the values of the transformed image [100]. Thus, its goal is to estimate the intensity at the new position [73] and depends on the motivation for registering the images. The accuracy and speed of the registration process can be improved through the use of suitable interpolation solutions. Nearest neighbor, linear interpolation or trilinear interpolation are the simplest interpolation methods, and consist of curve fitting using linear polynomials. Any other interpolation method beyond the nearest neighbor interpolation is required to guarantee accuracy. However, the resultant image will be smoother than the original. When the interpolation complexity increases, according the number of polynomial variables augments, smoothing effects can accumulate, or even generate artifacts [100]. Recent interpolation methods between neighboring slices in greyscale are based on B-splines [167], geometric multi-grid [168], using a modified control grid interpolation algorithm [169] or adaptive 2D autoregressive modeling and soft-decision estimation [170]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 35 The interpolation error can introduce modulations in the similarity measure, since transformations involve pure translations of datasets with equal sampling spacing, and the period of the modulation is the same as the sampling spacing. Thus, interpolation methods must be used with practicable computational costs, firstly using a low cost interpolation as trilinear or nearest neighbor. It is a good practice to employ a more expensive interpolation in the last few iterations or even take advantage of the spatial-frequency dependence of the interpolation error, such as cubic B-splines or windowed sinc interpolators. It must be taken into account the level of smoothness and robustness of the similarity measure against artifacts, which may require a more robust interpolation solution to be used successfully in the optimization step. 3.3. Accuracy Assessments and Validation Image registration methods must be validated, especially in medical applications, through a verification process based on the comparison of results obtained against a gold standard. Accuracy assessment and validation imply a very low failure rate and high accuracy, through the knowledge of a ground truth registration [171]. The target feature is any object that can be localized independently of the view. The disparity in the two corresponding positions of the target feature after registration provides an upper bound on the root mean square (RMS) of target registration error (TRE) [172]. This measure of error is recommended to be used as the quantity of choice to be reported in the validation process. It can be expected to vary with the registration problem, since it comprises different image modalities, anatomical structures and pathologies, and distinct positions within a view [161]. Several fiducial features can be employed as registration cues as a more desirable method for rigid-body registration, constituting a validation standard. It can be determined without referring other standard validations and is accomplished through the exploitation of establishing statistical relationships among fiducial localization error (FLE) and TRE [173] to translate self-consistency into accuracy [161]. The software industry has already developed standards, protocols and quality procedures [174]. Validation usually follows a sequence of measurements using ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 36 computer-generated models, known as software generated phantoms [175] and images of patients or volunteers against with the registration algorithms must demonstrate competence. Experimental validation of an image registration system must be extended to a clinical situation [176]. Visual assessment is also used as a standard and recently subjected to validation. Based on registration circuits, a selfconsistency method [161] is considered where a set of three or more images are registered in pairs. Registration validation methods have been concentrating more efforts for rigid registration than for non-rigid registration [161]. Their improvements are fundamental so novel registration models can be accepted as a clinical tool, which is not possible without a means of validation method. 3.4. Image registration software packages Several registration methodologies have been developed [109], particularly for multimodality, cardiac and brain images registration, but also in whole-body oncological applications [177], which are commercialized with the nuclear imaging equipment or developed under their respective software, as Hermes Medical Solutions, GE Healthcare, Philips and Siemens, in a single unit depending on the specific clinical needs. The state-of-the-art of user friendly software oriented to medical image processing, segmentation and registration, respecting to the registration methods, rigid and non-rigid transformation as well as their main applications, optimization and interpolation algorithms is yet reduced, being the majority of the existing software directed to developers. A system for PET–MRI registration capable of automatic scalp/brain segmentation replacing manual drawing operations and a fast and accurate image registration method is embedded in a commercially available scientific visualization package [178]. A parallel implementation uses a priori information about the nature of imaged objects to adapt the regularization of the deformations, giving higher weight to those points in images that contain more information. Its usability was improved through the implementation of a grid service that can be controlled by a graphics workstation embedded in the clinical environment [138]. The Functional Image Registration (FIRE) is an operating system and platform for independent multimodal image registration software, where several automatic algorithms were implemented, including principal axes matching and maximization of the mutual ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 37 information methods; a user interface was designed to support image manual registration [174]. Insight Toolkit (ITK) is an object-oriented software system, implemented in C++, for image processing, segmentation and registration. It is an open-source software used to academic research, once it is designed to be intuitive and easy to learn through a basic object-oriented and implementation methodology, although being a large and complex system, by exploring the examples available within the source directory. This cross-platform system provides developers an extensive suite of software tools for image analysis to employ leading-edge algorithms for registering and segmenting multidimensional data [179]. There are various registration software packages related with this toolbox. A well-known software based on ITK is Elastix [180]. It registers any type of images, but is frequently used to medical image registration. Supporting many transform models, similarity measures, optimization methods, interpolation methods, and multi-resolution schemes, it facilitates the construction of own user registration methods since their components can easily be plugged in. Advance Normalization Tools (ANTs) also depends on the ITK and extracts information from complex datasets that include imaging, being useful for managing, interpreting and visualizing multidimensional data. It has been considered an emerging tool supporting standardized multimodality image analysis [181]. A software developed in ObjectiveC oriented to MacOS called OsiriX provides multidimensional image navigation and image display to interpretation of large sets of multidimensional and multimodality images [182]. The image processing and visualization tools VTK, also based on ITK, have graphic capabilities provided by Open Graphics Library (OpenGL) graphic standard. It is thought to simplify the navigation through large datasets, such as to do complex and specific tasks [182]. NiftyReg belongs to the NifTK platform, developed at University College of London, and is capable of perform rigid, affine and non-linear registration of nifty or analyze images. Specifically oriented to groupwise and longitudinal registration, Groupwise and Longitudinal Image Registration Toolbox (GLIRT) is useful for unbiased analysis of a large set of MRI brain images, including improved unbiased groupwise registration guided with the sharp group-mean image, and hierarchical feature-based groupwise registration with implicit template. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 38 3D-Doctor supports greyscale and color MRI, CT and PET images in several formats and provides segmenting tools, 3D modeling export, measurements and quantitative analysis, 3D advanced processing tools. Through registration and fusion tools, the end-user can visualize re-sliced images automatically or semiautomatically using a user-defined axis. Automated Image Registration (AIR) is a library that allows automated intra and inter-subject registration of 2D and 3D images, such as mono and multimodality registration. Frequently used on academic research, Matlab Image Registration Toolkit (MIRT) is a software package for 2D and 3D non-rigid image registration, supporting mutual information (MI), residual complexity (RC), sum of squared differences (SSD), sum of absolute differences (SAD) and correlation coefficient (CC) as similarity measures, as well as parametric and non-parametric transformation models, namely free form deformation (FFD) and curvature regularization. To the optimization step, it presents implicit Euler method (gradient-based) and regulates with penalized Laplacian of the displacements both for parametric and non-parametric transformation models. Multi-resolution and groupwise registration is possible. However, compared with ITK, Matlab is heavier so the application will have a higher processing time. Amide is a Medical Image Data Examiner (AMIDE) that has been developed to be user-friendly to display and analyze multimodality volumetric medical images. It enables the user to freely shift, rotate, view, and analyzes data sets while the program automatically handles the interpolation needed. It is compatible with UNIX, Macintosh OS X and Microsoft Windows platforms [183]. Based on Matlab, Statistical Parametric Mapping (SPM) is a software package designed for the analysis of brain imaging data sequences as series of images from different cohorts or time-series from the same subject [184]. It enables the construction and assessment of spatially extended statistical processes, used to test hypotheses about functional imaging data. However, this software has lost its popularity to BioImageSuite [185]. This software has extensive capabilities for cardiac, abdominal and neuro-imaging analysis providing functionality for image visualization and registration, surface editing, cardiac 4D multi-slice editing, diffusion tensor image processing and mouse segmentation and registration. Moreover, it can be integrated with other biomedical image processing software. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 39 3.4.1. Registration methods available in ITK The ITK registration framework is based on a data flow via pipeline, where each component applies a specific operation at the inputs, being its outputs equally treated by another element, consisting of a sequence of pointers with specific attributes that are linked each other to perform various operations on a dataset. Table 2.2. Available registration functions in ITK-4.3, relevant for this report understanding [179]. Funtion Class Description Transform B-Spline Uses as template parameters the type for coordinates representation, the dimension of the space, and the order of the B-spline. Transform Versor Rigid 3D Implements a rigid transformation in 3D space, exposing six parameters, three for the versor components and three for the translational components. The center coordinates are not modified during the optimization performed in a registration process. Transform Affine Represents an affine transform composed of rotation, scaling, shearing and translation. The transform is specified by a N × N matrix and a N ×1 vector where N is the space dimension. Only defined when the input and output space have the same dimension. Metric Mattes Mutual Information The marginal and joint probability density function (PDF) is evaluated at discrete positions or bins uniformly spread within the dynamic range of the images. Entropy values are then computed by summing over the bins. Interpolation B-Spline Represents the image intensity using Bspline basis functions. When an input image is first connected to the interpolator, Bspline coefficients are computed using recursive filtering (assuming mirror boundary conditions). Intensity at a nongrid position is computed by multiplying the B-spline coefficients with shifted Bspline kernels within a small support region of the requested position. Interpolation Linear Assumes that intensity varies linearly between grid positions. Unlike nearest neighbor interpolation, the interpolated intensity is spatially continuous. However, the intensity gradient will be discontinuous at grid positions. Optimizer LBFGS Limited memory Broyden, Fletcher, Goldfarb and Shannon minimization. Optimizer Regular Step Gradient Descent Advances parameters in the direction of the gradient where a bipartition scheme is used to compute the step size. Optimizer Versor Rigid 3D Transform Optimizer Specialized version of the regular step gradient descent optimizer for versor rigid 3D transform parameters, where the current rotation is composed with the gradient rotation to produce the new rotation versor. The translational part of the transform parameters are updated as usually done in a vector space. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 46 performed according to the equation 4.1. Non-linear image intensity normalization is employed when the pretended intensity normalization function is a non-linear equation [206]. 𝑔(𝑥,𝑦) = 𝑚𝑎𝑥 {𝑔(𝑥,𝑦)}−𝑚𝑖𝑛 {(𝑔(𝑥,𝑦)} 𝑚𝑎𝑥 {𝑓(𝑥,𝑦)}−𝑚𝑖𝑛 {𝑓(𝑥,𝑦)} (𝑓(𝑥,𝑦) – 𝑚𝑖𝑛{𝑓(𝑥,𝑦)}) + 𝑚𝑖𝑛{𝑔(𝑥,𝑦)} (4.1) 4.2.2. Image resampling It is possible to enlarge an image as it is pretended. It is needed to create the grid with the intended size. If the pixel spacing defined is the same as the original, then the shrunken image fits exactly over the original image. Note that the pixel spacing in the shrunken grid will be less than the pixel spacing in the original image. Image interpolation is used to assign point intensities in the overlay grid [207]. 4.2.3. Image interpolation Tasks as zooming, shrink, rotating and perform geometric corrections uses image interpolation as basic tool. It is the process of using known data to estimate values at unknown locations [208]. The nearest neighbor interpolation consists of assigning to each new location the intensity of its nearest neighbor in the original image. Still a simple process, it introduces undesirable artifacts, such as distortion of edges. To overcome this problem, more suitable approaches are employed. They are bilinear and bi-cubic interpolation, which uses four and sixteen nearest neighbors, respectively, to estimate the intensity of a given location. Bi-cubic interpolation allows a better preservation of fine details, besides the higher processing time, which is justifiable for medical image processing. (a) (b) Figure 4.3. Image interpolation results: (a) application of nearest neighbor interpolation and (b) using bilinear interpolation [206]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 47 Figure 4.3. presents images that were zoomed from 128 x 128 to 1024 x 1024 pixels using nearest neighbor interpolation and using bilinear interpolation, which clearly shows better improvements for bilinear interpolation technique. More complex interpolation techniques, such as splines and wavelets can be used to obtain better results [209]. A B-spline interpolation consists of a basis spline function that has minimal support with respect to a given degree, smoothness and domain partition, i.e., any spline function of a given degree can be expressed as a linear combination of B-splines of that degree. Spline interpolation is preferred over polynomial interpolation since its error can be less if using a low degree. Moreover, it avoids the problem of Runge’s phenomenon, consisting of oscillation at the edges on an interval that occurs when using polynomial interpolation of high degree [207]. 4.2.4. Image averaging Nuclear medicine images can contain noise, deterioration factors, spatial resolution and image reconstruction techniques, as well as they are dependent on the behavior of the patient respecting the clinical protocol. (a) (b) Figure 4.4. Noise reduction of (a) X-ray image of circuit board corrupted by salt-and-pepper noise, using a 3 x 3 averaging mask, resulting in image (b) [206]. Therefore, it is fundamental to reduce the noise content. Smoothing filters are usually employed, which masks yields the standard average of the pixels under the mask. A 𝑚 𝑥 𝑛 mask would have a normalizing constant equal to 1/𝑚𝑛. If all coefficients are equal, the averaging mask is also called a box filter [175]. An example of its application is shown in Figure 4.4. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 48 4.2.5. Morphological Image Processing Object shape description and its structure properties are defined as morphology. Mathematical morphology is used to extract image properties. Its methods are used for image processing, namely morphological filtering, thickening or thinning [179]. Morphological operations require, as input data, both the processed image and a structural element, whose shape and dimension is arbitrary and can be represented as a binary image of a given size. The structural element is applied to all pixels of binary image and its origin is combined with a single binary pixel. Consequently, the entire structural element is wrapped and a subsequent alteration of the corresponding pixels of binary images occurs. Erosion and dilation are the simplest morphological operations used to image processing. Erosion consists of turning on the corresponding pixel to the origin of the structure element B if the entire structure element falls with foreground area of a set A; it “contracts” the boundary of A. Dilation consists of turning on the corresponding pixel to the origin of the structure element B, if the entire structure element overlaps the foreground area of a set A by at least one element; it “expands” the set A. Morphological opening is the dilation of the erosion of a set A by a structuring element B. It is used for smoothing contours, breaking narrows isthmuses and removes small islands or sharp peaks. On the other hand, morphological closing of a set A by a structuring element B is defined as the erosion of the dilation of that set. It is employed when is intended to smooth contours, fuses narrow breaks and long thin golfs, eliminating small holes too. These morphological operations are illustrated in Figure 4.5. They are frequently combined to remove small objects or holes, respectively, and are one of the basic operations of morphological noise removal [180]. Hit or miss transform, boundary extraction, connected components, convex hull, thinning, thickening, skeletons, pruning, holes filling, border clearing or topand bottom-hat operations are examples of morphological operations. Top-hat is the difference between the input and the output of an opening operation; it enhances the thin sharp positive variations. On the other hand, bottom–hat is the difference between the output of a closing operation and the correspondent input image [206]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 49 Figure 4.5. Morphologic operations results of opening and dilation using object A (top row). The structuring element is the small circle, whose dot is its center. Opening operation consists of the application of erosion (second row) followed by dilation (third row). Closing operation consists of the application of dilation (forth row) followed by erosion (fifth row). 4.3. Image segmentation Image segmentation is defined as the process of partitioning an image into multiple sets of pixels, known as segments, and allows the simplification or change in the representation of an image into regions of interest. The level of the subdivision depends on the problem being solved. It subdivides an image into its constituent regions, or objects, or a set of contours, through the attribution of a label to each pixel. The pixels of a segmented region are similar with respect to some computed property sharing the same label, but adjacent regions are significantly different. Image segmentation algorithms are generally classified as intensityor regionbased. The first approach consists of partitioning an image based on abrupt changes ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 50 in intensity, such as edges, while the second category relies on regions that are similar according to a set of pre-defined criteria. The several applications of image segmentation cover areas as industry, biology, video surveillance, recognition, traffic control system, biology and microscopy, content-based image retrieval, machine vision, and medical imaging. It is a fundamental tool to locate tumors and other pathologies, measure tissue volumes, diagnosis and study of anatomical structure, surgery planning, virtual surgery simulation and intra-surgery navigation. Some techniques were tested in the experimental implementation presented in this dissertation, namely Otsu method, k-means clustering, region growing and shape detection, to compare these approaches in myocardial perfusion SPECT images. These methods are explained next. 4.3.1. Otsu thresholding Thresholding is the simplest and one of the most used methods of image segmentation due to its intuitive properties and simplicity of implementation, whereupon a threshold value separates the objects intended to be extracted from the background. Then, being 𝑇 the select threshold, any point (𝑥,𝑦), for which 𝑓(𝑥,𝑦) > 𝑇, is called an object point. Otherwise, it belongs to the background, called a background point. Depending on the threshold values, the type of thresholding varies, i.e. if the method only depends on gray-level values, it is a global thresholding, but if it also depends on some local property, it is called a local thresholding; a dynamic or adaptive threshold is employed if the threshold value depends on spatial coordinates. Otsu method is based on thresholding and it is used to automatically perform clustering-based image thresholding or the reduction of a grey level image to a binary image (see Figure 4.6). It assumes that the image to be threshold has a bimodal histogram, so it calculates the optimum thresholding that separates those two classes. First, it selects the initial threshold T and segments the two groups of pixels. The algorithm computes the histogram and the probabilities of each intensity level and sets up both initial class probability and respective mean. It updates the threshold 𝑇 considering the mean intensities previously calculated. Then, the process is repeated until the difference between two successive threshold values is less than ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 51 a prescribed tolerance. The optimum threshold is the one that minimizes the intraclass variance and maximizes the inter-class variance. (a) (b) Figure 4.6. Application of Otsu thresholding method on a clear bi-modal image (a), resulting in a well segmented image (b). The Otsu threshold can be extended to multiple thresholding levels, which is the process of segmenting a gray level image into several distinct regions. It enables the determination of more than one threshold, segmenting the image into one background and several objects, each one at different intensity levels. It can be obtained good results with images that have modal intensity levels well defined. 4.3.2. K-Means Clustering K-Means clustering algorithm is a segmentation method that classifies the input data points into multiple classes based on the distance from each other. The algorithm assumes data features from a vector space and finds the subsequent clusters, through their centroids. Accordingly, it is a method of vector quantization that aims partitioning 𝑛 observations into 𝑘 clusters, whose observation belongs to the cluster with the nearest mean. The main applications of this method are vector quantization, cluster analysis and feature learning. It is exemplified in Figure 4.7. This method relies on convergence to a local minimum, which may produce counterintuitive results. Furthermore, an inappropriate choice of the number of clusters 𝑘 may yield poor results, if the number of clusters in the data set is quite different. Unfortunately, the facts of both the Euclidean distance being used as metric and variance as measure of cluster scatter are features that makes k-means as efficient as limited. Several variations of this algorithm have been developed due to overcome computational complexity and time consuming. Some examples are the following methods: Jenks natural breaks optimization, k-medians clustering, k-medoids, fuzzy ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 52 C-means clustering, Gaussian mixture models with expectation-maximization algorithm, kd-trees, spherical k-means or even minkowski metric weighted k-means. (a) (b) (c) Figure 4.7. (a) HLA myocardial perfusion slice. (b) Segmentation using k-means (3 clusters). (c) Segmentation using k-means (5 clusters). Note that an inappropriate choice of the number of clusters 𝑘 may yield poor results, if the number of clusters in the data set is quite different. 4.3.3. Region growing Region growing is an unsupervised region-based image segmentation method that groups pixels or sub-regions based on both predefined similarity and stopping criteria. The algorithm starts with a single pixel or set of pixels defined as seed points, from which the segmented region grows according to pre-defined conditions of similarity between the seeds and their neighboring pixels. The selection of similarity criteria depends on the problem under study and the type of available data. The formulation of a proper stopping rule, that stops the region growing from the seeds when no more pixels satisfy the inclusion criteria, is one of the major difficulties of this method (see Figure 4.8). (a) (b) Figure 4.8. Segmentation of (a) HLA myocardial perfusion slice using region growing method, resulting in image (b). The difficult definition of the stopping criteria can result in lack of accuracy. Image segmentation methods based on region growing can separate regions with the same properties, but requires high power and time consuming. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 53 4.3.4. Level set methods Level set method is based on implicit representation of the interface. It is a numerical technique for tracking interfaces and shapes, since it can perform numerical computations involving curves and surfaces on a fix grid without having to parameterize these objects. It enables segmentation of time-varying shapes. The main advantages of the level set methods are the fact that topological changes are handled smoothly with no user intervention required, as well as corners and cusps, using methods borrowed from hyperbolic conservation laws. Moreover, the method is easily extended to higher dimensions [175]. The fast marching method is related to the level set method, but solves a given problem much more quickly. It also uses an implicit representation for an evolving interface, but the embedding function carries much more information. This method requires the entire evolution of the interface to be encoded in the embedding function. This enables a faster solvation of the problem with one single pass over the mesh, contrasting with the level set method where each time steps requires an additional pass over the mesh to evolve the level set function in time. The fast marching method needs an initialization that must be selected closed to where the exact solution is assigned, consisting of all the nodes that are immediately adjacent to the initial interface. Higher degree of accuracy can be reached using a bi-cubic interpolation function. It is not just used to obtain accuracy for the distance to the zero level set, but also for sub-grid resolution of the shape of the interface and sub-grid resolution of the level set function. Therefore, re-initialization is employed to reconstruct the level set function to be the signed distance function, i.e., it fixes the level set function when the velocity field does not preserve the level set function as a signed distance function. An alternative is to adjust the velocity field in the first place. The fast marching method has made a contribution to several application, like crack propagation, shape reconstruction, image processing, medical imaging, computer graphics and visualization and robotic navigation [179]. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 54 4.4. Image Quantitative Analysis Image analysis can be defined as the extraction of meaningful information from images. Shape descriptors are used in a great number of image processing applications due to their capacity of characterization of the regions of interest. The reason for a permanent interest for newly created shape descriptors relies on the demand for more efficient shape classification procedures. 4.4.1. Labeling Extracting and labeling of various disjoint or connected point in an image is fundamental to automated image analysis applications. The algorithm starts by scanning a binary or grayscale image, pixel-by-pixel, from both left to right and top to bottom. A label is attributed to each pixel, and groups the pixels into components based on pre-defined pixel connectivity. The equivalent label pairs are stored in an equivalent matrix, or into equivalence classes, and a unique label is assigned to each class. Finally, a second image scan replaces the labels previously assigned by the label assigned of its equivalence class. Then, all connected component pixels share the same label. The labeled objects, or even only their boundaries, are often displayed with different gray levels or colors, as illustrated in Figure 4.9. Figure 4.9. Identification of three objects through different color labels. 4.4.2. Extraction of geometric dimensions After segmentation and connected components labeling, the objects of interest may be described through shape parameters, namely elementary geometrical parameters. The parameters used in the present dissertation will be now exposed. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 55 The perimeter can be obtained from the chain code of the object boundary, taking into account the length of the chain code and considering that all steps in diagonal directions are longer by a factor of 2. For an 8-neighborhood chain code the perimeter is given by the equation 4.2, where 𝑛𝑒 and 𝑛𝑜 are respectively the number of even and odd chain code steps. 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 𝑛𝑒+ √𝑛𝑜 2 (4.2) Perimeter results directly from the construction of the boundary line with equidistant samples and is well approximated to the number of sampling points times the mean distance between the points. Note this shape perimeter is sensitive to noise, so comparison of perimeters from different images must be realized carefully. However, it does not depend on the orientation of the objects on the image plane. Roundness, or circularity of a region, is a geometric feature that is invariant under translation, rotation and scaling. Given an object R, the circularity is given by function 4.3, where 𝐴 represent the object area, i.e, the number of pixels within the object, and 𝑃 its perimeter. It results in the maximum value of 1 for a perfect round region and a value in the range between 0 and 1 for all other shapes. This shape descriptor also offers information on how regular an object is, because the inverse of this measurement defines the compactness factor (see eq. 4.3). 𝐶𝑅 =4𝜋𝐴 𝑃2 (4.3) Equivalent spherical radius of an irregularly-shaped object is the equivalent radius of a hypersphere of the same size than the label object, which value depends on the image spacing. Elongation is a basic shape descriptor with a clear intuitive meaning. Its standard measure is area-based because all points belonging to the shape are involved in its computation. It is derived from the shape orientation definition which is based on the axis of the last second moment of inertia. Therefore, it is the ratio of the largest principal moment to the second largest principal moment. Its value is greater or equal to 1. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 62 5.1. Implementation The computational solution was fully implemented in C++ and tested on a notebook PC with Intel® Pentium® CPU P6200 2.13GHz processor, RAM 4.0GB, NVIDIA® GFORCE® with CUDA® 315M graphic, Samsung SSD 840 Series with 100 GB and a TOSHIBA MK3252GSX with 300 G and under Microsoft Windows 7 NT operating system (32-bits). Computational techniques of image segmentation, processing and classification were implemented using the free open source toolkits Insight Toolkit (ITK) 4.3. 5.2. Material and methods 5.2.1. Dataset Data used in the preparation of this dissertation were provided by Hospital Lusíadas Porto, Porto, Portugal. The control group contains female and male stress and rest gated myocardial perfusion SPECT images. The dataset is formed by 180 3-D images from 48 patients with healthy cardiac condition and 72 3-D images from 12 patients with associated cardiac diseases. Data was provided in DICOM multi-frame image format. The image acquisition system was a single head e-cam SPECT camera (SIEMENS-Germany) equipped with a low-energy high resolution collimator. The data from the SPECT studies was acquired in 64 × 64 image matrix for 32 projections over 180◦ arc, 25s per projection, from 45◦ right anterior oblique (RAO) to the 45◦ left posterior oblique (LOP). These images were reconstructed using the filtered back projection algorithm and a low pass Butterworth filter (cut off: 0.4-order: 5). Thereafter, semi quantitative analysis of LV myocardium perfusion has been done by Cedars-Sinai Software (20 segment model). 5.2.2. Template myocardial SPECT image The template myocardial SPECT image is built as a consistent reference against with it will be compared the images to be classified. Its formation requires three distinguished steps, namely (1) image registration of healthy patients’ images, ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 63 (2) segmentation of LV, (3) coronary artery mapping and (4) registration of image obtained in step 1 with the coronary artery mapping image obtained in step 3. The template image is composed of 12 slices for each cardiac axis, there being a template image for stress and rest clinical protocol. The stress template myocardial SPECT is the result of 16 healthy patients and rest template image corresponds to the registration of 6 patients’ exams (these patients are the same of the stress dataset used for building the template image). This difference is due to the fact that the patients firstly realize the stress protocol and the rest protocol is not always necessary, there being a few number of rest protocol images. At the end, there are built three template images per clinical protocol (rest or stress), one for each axis (SA, VLA and HLA), consisting of the registration of myocardial SPECT images from healthy patients containing the coronary artery mapping, performing a total of six template myocardial perfusion SPECT images. 5.2.2.1. Healthy myocardial SPECT image registration To build the 3-D template SPECT image, an image from the dataset was selected to be the reference image. Then, the data of the control group was automatically registered with the reference image. The result of the registration process was defined as the template image. Note that the template image is built just once. The full algorithm is presented in Figure 5.1. Cardiac structures have different dimensions for each patient, and more significantly depending on the patient genre, i.e., as the image is from a female or male patient. Then, it is fundamental that the moving image pass through a cubic BSpline interpolator to set the origin, spacing, direction and size features of the fixed image. A rescale intensity image filter is used next to normalize both images intensities. Hereafter, the registration method is implemented. It is divided into a preregistration method based on rigid transforms and a registration method based on deformable transforms, both using multi-resolution registration technique, since it is faster and efficient. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 64 (a) Image pre-processing Registration based on deformable transforms using multi-resolution registration technique Pre-registration based on rigid transforms using multi-resolution registration technique Conversion of DICOM multi-frame images into DICOM volumes 3-D Template myocardial perfusion SPECT image Image intensity normalization B-Spline interpolation Versor rigid 3D transform, Mattes mutual information metric, versor rigid 3D optimizer and B-Spline interpolator B-spline transform, Mattes mutual information, LBFGS optimizater and B-spline interpolation (b) (c) (d) (e) (f) Figure 5.1. Algorithm framework and images’ examples obtained at each step: (a) algorithm framework implemented to generate a template myocardial perfusion SPECT image; (b) input 3-D image; (c) Bspline interpolation 3-D result; (d) rescale intensity image filter 3-D result; (e) image pre-registration 3D result; (f) image registration 3-D result. The pre-registration method consists of an initial translational preregistration step. A centered transform initializer uses the center of mass given by the image intensities of input images. Then, it is applied a rigid 3D transform consisting of a 3D rotation and a 3D translation, specified by a versor and a vector, respectively. The similarity measure used is the Mattes mutual information, based on information theory, which consists of measuring how much information in one random variable tells about another variable using one set of intensity sample to evaluate the marginal and joint probability density function at discrete positions. The optimizer that searches for the best geometric transformation is the versor rigid 3D transform optimizer that implements a gradient descent optimizer for the transformation parameter space. The employed interpolator is the cubic B-Spline interpolator. The main parameters defined to properly perform this pre-registration ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 65 algorithm described are presented in Table 5.1. These values were experimentally obtained, through trial and error. After obtaining the pre-registered image, a final registration step based on deformable transformation is applied, to register it with the reference image. Table 5.1. Main parameters’ values defined in the pre-registration algorithm of healthy myocardial SPECT images. Function Parameters Values Metric Number of histogram bins 128 Metric Number of spatial samples 25000 Optimizer Translation scale 100000 Optimizer Number of iterations 100 Optimizer Maximum step length 0.05 Optimizer Minimum step length 0.005, if multi-resolution level = 0. 0.00005, if multi-resolution level > 0. Multi-resolution registration Number of levels 3 The registration method starts with a B-Spline transform that encapsulates a deformable transform of points from one 𝑛-dimensional space to another 𝑛dimensional space. The Mattes mutual information is also used as similarity measure. The optimizer used here is a LBFGSB optimizer, which minimizes a nonlinear function 𝑓(𝑥) of 𝑛 variables subject to simple bound constraints. Then, it is employed a BSpline intensity interpolator. The main parameters defined to perform properly the registration algorithm described are presented in Table 5.2. These values were experimentally obtained, through trial and error. 5.2.2.2. Segmentation of the LV and computation of related geometric dimensions The LV segmentation is implemented in 2D. The first step is to extract the DICOM volume’s slices obtained in the previous registration step. Due to the image acquisition system, DICOM images have low resolution. It is partially improved passing the template image by a resample image filter that sets the default pixel value to 10 and an output spacing factor of 0.3. Next, the images are post-processed using mean spatial filtering, to reduce the noise of the images, followed by morphological operations. Opening and closing operations were used to implement a top hat followed by a bottom hat. The obtained image is added to the slice, and then the bottom hat is subtracted. This ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 66 step improves the gradient magnitude of the template SPECT image’s slices. Posteriorly, k-means clustering using 3 clusters is employed. Table 5.2. Main parameters’ values defined in the registration algorithm of healthy myocardial SPECT images. Function Parameters Values Metric Number of histogram bins 128 Metric Number of spatial samples (Number of pixels of the fixed region * 20.0 )/ 50.0 Metric Translation scale 100000 Optimizer Number of iterations 100 Optimizer Relaxation factor 0,9 Optimizer Cost function convergence factor 1e9, if multi-resolution level = 0. 1e14, if multi-resolution level > 0. Optimizer Projected Gradient Tolerance 1e-9, if multi-resolution level = 0. 1e-14, if multi-resolution level > 0. Optimizer Number of iterations 200 Optimizer Number of Evaluations 400 Optimizer Number of Corrections 50 Interpolator Number of grid nodes in one dimension 10 Interpolator Spline order 3 Multi-resolution registration Number of levels 3 Here, the LV is already segmented. A label map filter is applied and the contour of each object is obtained. Object related geometric dimensions are computed, specifically perimeter, equivalent spherical radius, roundness, elongation and number of pixels. Each geometric dimension is written into a vector. So, five vectors are obtained, constituting the set of features from myocardial perfusion SPECT images that has been initially proposed to aim. Figure 5.2 illustrates this algorithm. 5.2.2.3. Coronary artery mapping The next step consists of generating the coronary artery mapping of the template image previously obtained, which posterior alignment with images under study will allow the clinical expert to observe the localization of cardiac abnormalities. To perform this task, the 20 segment-based coronary artery mapping was manually drawn for the apical, medial and basal region of the template myocardial perfusion SPECT image of each axis ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 67 (a) Image post-processing Conversion of DICOM volumes into DICOM slices Image Segmentation Computation of geometric related dimensions Segmented LV Structures Image averaging and morphological image processing. K-means clustering Perimeter, equivalent spherical radius, roundness, elongation and number of pixels. (b) (c) (d) Figure 5.3. Segmentation algorithm: (a) segmentation algorithm framework; (b) input 3-D image (c) 3-D image result of image averaging followed by morphological processing techniques; (d) example slice of segmented myocardial perfusion using k-means 3 clusters. 5.2.2.4. Registration of coronary artery mapping This is the last step required to build the template coronary artery mapping of myocardial perfusion SPECT image. Similar algorithms to those described in section 5.2.2.1 were used to align the coronary artery mapping image slices, obtained in the previous step, with the template image obtained in section 5.2.2.1. Accordingly, it is also divided into a pre-registration method based on rigid transforms and a registration method based on deformable transforms, both using multi-resolution registration technique. The registration algorithm was implemented bi-dimensionally, since the input images are the 2-D segmented images previously ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 68 obtained. The algorithm employed and registration components are synthesized in Figure 5.3. Here, the pre-registration method starts with the same centered transform initializer used in section 5.2.2.1. Then, it is applied an affine transform, a linear transformation that maps lines into lines. As previously, the similarity measure employed is the Mattes mutual information. According the transform method employed, a regular descent optimizer is used. These components are combined with a linear interpolator. The main parameters defined to perform this pre-registration method are presented in Table 5.3. These values were experimentally obtained, through trial and error. (a) Image pre-processing Segmented template image’s slices and template coronary artery mapping slices Pre-registration based on rigid transforms using multi-resolution registration technique Registration based on deformable transforms using multi-resolution registration technique Coronary artery mapping segments labelling Template image containing coronary artery mapping B-Spline interpolation Image intensity normalization Affine transform, mattes mutual information, regular step gradient descent optimizer and linear interpolation B-spline transform, mattes mutual information, regular step gradient descent optimizater and B-spline interpolation Image segmentation K-means clustering (3 clusters) (b) (c) (d) Figure 5.2. Pre-registration algorithm used to align the template image's slices with the corresponding coronary artery mapping; (b) Image to be aligned; (c) Pre-registration between the input image and the coronary artery map obtained; (d) Coronary artery mapping registration final output. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 69 The pre-registration algorithm’s output is the image under study with the coronary artery mapping. Therefore, a final registration step based on deformable transformation is applied, to register it with the coronary artery mapping of the template image. The final registration algorithm is based on multi-resolution registration approach. It is compound by the B-Spline transform, the Mattes mutual information metric, the regular step gradient descent optimizer and the B-Spline intensity interpolator. The main parameters used to perform the method were experimentally obtained, presented in Table 5.3, through trial and error. Table 5.3. Main parameters’ values defined in the pre-registration algorithm used for aligning the template myocardial perfusion SPECT images with the coronary artery mapping. Function Parameters Values Metric Number of histogram bins 128 Metric Number of spatial samples 50000 Metric Translation scale 100000 Optimizer Number of iterations 200 Optimizer Relaxation factor 0,8 Optimizer Maximum step length 0.5, if multi-resolution level = 0. Optimizer Minimum step length 0.05, if multi-resolution level = 0. 0,0005, if multi-resolution level > 0. Multi-resolution registration Number of levels 3 Table 5.4. Main parameters’ values defined in the registration algorithm used for aligning the template myocardial perfusion SPECT images with the coronary artery mapping. Function Parameters Values Metric Number of histogram bins 50 Metric Number of spatial samples (Number of pixels of the fixed region * 60.0 )/ 100.0 Metric Translation scale 100000 Optimizer Number of iterations 200 Optimizer Relaxation factor 0.9 Optimizer Maximum step length 10 Optimizer Minimum step length Tolerance 0.1 Optimizer Number of iterations 200 Interpolator Number of grid nodes in one dimension 7 Interpolator Spline order 3 Multi-resolution registration Number of levels 3 ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 70 5.2.3. Myocardial SPECT image segmentation and registration The computational techniques explained before, used to segment the LV and its registration with the template image, are also used to register the image under study with the template image. The complete algorithm is summarized in Fig. 5.4. The first step consists of defining the first and last slice of interest, to segment and register only the slices with relevant information. The empirical analysis of image datasets has proved the first and last fifths of DICOM volumes do not contain relevant information. Accordingly, the algorithm was programmed to consider the first slice of the second fifth of the volume as the first slice to be analyzed and the last slice of the forth fifth of the volume as the last slice. Secondly, the image under study is segmented based on k-means clusters using 3 clusters and respective geometric dimensions are computed, using the algorithm described in section 5.2.2.2. This step enables clinical professionals analyzing the myocardial perfusion of the patient, providing a better visual evaluation of myocardial perfusion extent. Note since the algorithms of image processing, registration and segmentation had already been exemplified through images previously and the following framework applies the same techniques, there is no need of exemplifying the next processes. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 71 Image pre-processing Image pre-processing Patient exam’s (image under study) Pre-registration based on rigid transforms using multi-resolution registration technique Registration based on deformable transforms using multi-resolution registration technique Image under study containing the artery coronary mapping with template myocardial perfusion SPECT image dimensions. Image Segmentation Segmented LV Structures Definition of both first and last slice Computation of geometric related dimensions Image averaging and morphological image processing. K-means clustering (3 clusters) B-Spline interpolation and Image intensity normalization Affine transform, mattes mutual information, regular step gradient descent optimizer and linear interpolation B-spline transform, mattes mutual information, regular step gradient descent optimizater and B-spline interpolation Image Segmentation K-means clustering (3 clusters) Perimeter, equivalent spherical radius, roundness, elongation and number of pixels. Figure 5.3. Segmentation and registration of patient’s exam. Image segmentation provides an accurate visual analysis and image registration of the patient’s exam with the template image enables a correct computation of related geometric dimensions according to the normal heart size. Note that the template image slices is chosen according the clinical protocol and axis of the image under study. As referred before, due to different hearts size between patients and depending on the genre, the computation of cardiac geometric related dimensions would lead to a lack of pattern from healthy and unhealthy geometric dimensions of myocardial perfusion region. It is predictable that healthy myocardial perfusion patients have higher geometric dimensions and unhealthy patients have small myocardial perfusion regions. However, a bigger LV can have considerable geometric dimensions but be unhealthy as well as a smaller structure, very common in women, can be healthy with smaller geometric dimensions. For this reason, it is fundamental the image under study to be registered with the coronary artery mapping slices. It is done using the same algorithm of section 5.2.2.4. The cardiac structure under study is interpolated considering the origin, ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 78 Table 5.6. Dice’s coefficient computation between a manual segmentation of a clinical expert and five automated methods (continuation). ITKSNAP Otsu Multiple-threshold K-means Clustering Region Growing Shape Detection 0.7504 0.4386 0.7545 0.8584 0.4834 0.6209 0.7359 0.9179 0.8579 0.6378 0.5732 0.7025 0.6836 0.6871 0.5504 0.5269 0.5220 0.5507 0.5784 0.4433 0.5303 0.4470 0.5386 0.5381 0.2381 0.4434 0.3708 0.6807 0.4678 0.2555 0.3956 0.1366 0.6247 0.5351 0.0212 0.3342 0.0574 0.4719 0.3191 0.1339 0.7093 0.4945 0.4123 0.6701 0.1913 0.7330 0.5700 0.5546 0.6887 0.2883 0.7004 0.7401 0.7084 0.7775 0.3754 0.7028 0.6575 0.8940 0.8578 0.4093 0.6938 0.6722 0.8868 0.8646 0.5095 0.6718 0.7584 0.8653 0.9174 0.4796 0.6586 0.7700 0.8512 0.9159 0.5692 0.6645 0.8151 0.9732 0.9117 0.6461 0.6228 0.7405 0.9219 0.8414 0.6462 0.4995 0.7054 0.8191 0.6867 0.4022 0.4667 0.7440 0.6509 0.4872 0.3502 0.0486 0.5472 0.5668 0.7097 0.5088 0.0722 0.0096 0.4296 0.3395 0.1662 0.1241 0.4549 0.5084 0.4911 0.4833 0.2741 0.7876 0.6916 0.6603 0.5809 0.4196 0.8257 0.8357 0.8392 0.4741 0.4887 0.7703 0.9023 0.9333 0.4189 0.5152 0.7015 0.9838 0.8439 0.3712 0.3507 0.6384 0.9265 0.9773 0.3560 0.4669 0.5515 0.9465 0.9010 0.3422 0.5314 0.4755 0.8251 0.8939 0.2650 0.5424 0.5153 0.8785 0.7838 0.1053 0.6479 0.5190 0.8496 0.8815 0.3794 0.6157 0.2533 0.6607 0.8664 0.3998 0.6618 0.3074 0.8459 0.6427 0.2499 0.0654 0.0000 0.8489 0.4302 0.0874 Mean 0.4844 0.5115 0.6970 0.6819 0.3673 It can be observed the Dice’s coefficient presents higher values for k-means algorithm. Thus, the segmentation of template myocardial SPECT slices using kmeans (3 clusters), shown in Figure 5.6-7, provides a more valuable computation of valuable myocardial perfusion region’s related geometric dimensions, namely ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 79 perimeter, equivalent spherical radius, roundness, elongation and number of pixels. Mean values of each geometric dimension per axis are shown in Table 5.7, for stress and rest template image. Table 5.7. Geometric dimensions of the segmented objects. Clinical protocol Axis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Stress SA 234.44 25.60 0.72 1.08 504.55 HLA 223.98 26.53 0.77 1.44 558.23 VLA 273.27 34.09 0.80 1.14 892.23 Rest SA 217.66 25.39 0.78 1.39 525.47 HLA 238.65 31.85 0.85 1.55 776.60 VLA 247.85 32.93 0.87 1.40 935.65 5.3.3. Bayesian classifier evaluation The classification algorithm used the geometric related dimensions obtained from segmentation step. Tables 5.8, 5.9 and 5.10 present the geometric dimensions obtained from the segmented structures and both Bayesian classification and clinical diagnosis. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 80 Table 5.8. HLA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis. Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 1 337.73 40.17 0.75 1.27 1237.54 Normal 388.47 38.82 0.65 1.74 299.44 Normal Normal Normal 2 318.62 38.70 0.76 1.25 1151.23 Abnormal 339.19 34.50 0.66 1.51 251.00 Abnormal Abnormal Abnormal 3 301.45 36.88 0.77 1.22 1039.89 Abnormal 364.93 37.30 0.67 1.57 283.29 Abnormal Abnormal Abnormal 4 349.54 43.49 0.78 1.32 1449.00 Normal 380.58 40.07 0.68 1.66 316.44 Normal Normal Normal 5 310.40 37.66 0.76 1.17 1093.92 Abnormal 310.60 34.26 0.69 1.58 247.07 Abnormal Abnormal Abnormal 6 349.90 40.82 0.74 1.37 1274.73 Normal Normal Normal 7 336.04 40.57 0.76 1.17 1261.00 Normal Normal Normal 8 324.71 39.39 0.76 1.23 1190.45 Normal Normal Normal 9 341.60 41.23 0.76 1.27 1310.23 Normal Normal Normal 10 314.44 38.33 0.77 1.24 1125.73 Abnormal Abnormal Normal 11 335.70 40.36 0.76 1.22 1260.07 Normal Normal Normal 12 318.75 38.42 0.76 1.27 1130.00 Abnormal Abnormal Normal 13 330.90 39.15 0.75 1.16 1173.00 Normal Normal Normal 14 347.31 40.27 0.73 1.43 1237.27 Normal Normal Normal 15 335.14 39.23 0.74 1.50 1170.89 Normal Normal Normal 16 319.41 38.87 0.77 1.17 1152.55 Normal Normal Normal 17 348.08 41.51 0.75 1.28 1328.80 Normal 369.16 39.50 0.67 1.69 308.24 Normal Normal Normal 22 401.53 47.30 0.74 1.37 1777.59 Normal 359.73 36.33 0.66 1.39 283.35 Normal Normal Normal 23 349.97 42.04 0.76 1.30 1381.87 Abnormal 392.79 40.79 0.67 1.62 331.78 Normal Abnormal Abnormal 24 363.68 42.97 0.74 1.31 1429.69 Abnormal 365.69 37.60 0.67 1.59 285.37 Abnormal Abnormal Abnormal (continues) ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 81 Table 5.8. HLA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis (continuation). Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 25 329.51 40.53 0.77 1.31 1276.54 Normal 365.69 37.60 0.67 1.59 285.37 Abnormal Abnormal Abnormal 26 368.82 43.04 0.74 1.29 1442.60 Normal 356.21 38.10 0.67 1.72 290.12 Normal Normal Normal 27 368.44 42.62 0.73 1.37 1402.56 Normal 410.10 42.02 0.66 1.69 345.27 Normal Normal Normal 29 364.38 43.77 0.76 1.23 1499.87 Normal 356.46 36.51 0.71 1.53 265.74 Normal Normal Normal 31 324.42 38.78 0.75 1.22 1148.85 Normal 374.63 38.74 0.67 1.73 300.46 Normal Normal Normal 33 366.21 42.49 0.73 1.50 1381.55 Normal 397.11 40.09 0.65 1.77 316.30 Normal Normal Normal 35 346.40 41.42 0.75 1.30 1310.30 Normal 395.90 40.61 0.66 1.64 329.60 Normal Normal Abnormal 36 366.21 42.49 0.73 1.50 1381.55 Normal 389.09 39.71 0.66 1.66 317.30 Normal Normal Normal 37 333.76 40.92 0.77 1.36 1279.60 Normal 379.19 39.24 0.67 1.67 310.35 Normal Normal Normal 38 354.38 41.58 0.74 1.25 1360.35 Normal 376.00 38.86 0.67 1.59 303.82 Normal Normal Normal 39 340.86 40.54 0.75 1.23 1283.33 Normal 383.55 40.36 0.68 1.60 325.98 Normal Normal Abnormal 40 339.75 40.94 0.76 1.23 1312.09 Normal 340.64 38.30 0.76 1.74 281.56 Normal Normal Normal 42 359.38 43.75 0.76 1.26 1532.59 Normal 388.19 40.83 0.68 1.65 332.71 Normal Normal Normal 43 354.01 41.87 0.75 1.31 1373.94 Normal 388.48 39.97 0.67 1.69 316.23 Normal Normal Normal 44 337.00 40.00 0.75 1.30 1248.07 Normal 376.36 38.28 0.67 1.70 294.24 Normal Normal Normal 45 313.91 38.16 0.76 1.18 1132.00 Abnormal 370.16 39.18 0.68 1.71 307.28 Normal Abnormal Abnormal 46 351.56 41.73 0.75 1.34 1350.73 Normal 407.26 41.25 0.66 1.76 335.68 Normal Normal Normal 47 365.11 43.50 0.75 1.40 1476.71 Normal Normal Normal 48 342.93 42.53 0.78 1.48 1402.47 Normal Normal Normal 49 355.48 41.85 0.74 1.54 1334.09 Normal Normal Normal 50 349.36 41.00 0.74 1.50 1290.92 Normal 341.52 37.32 0.69 1.68 280.53 Abnormal Abnormal Abnormal 51 329.60 39.49 0.75 1.31 1192.36 Abnormal 340.05 37.44 0.69 1.62 281.84 Abnormal Abnormal Abnormal (continues) ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 82 Table 5.8. HLA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis (continuation). Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 52 362.61 42.84 0.79 1.34 1315.22 Normal Normal Normal 53 336.66 41.16 0.88 1.47 1125.60 Normal 373.77 39.55 0.76 1.85 285.08 Normal Normal Normal 54 320.30 37.83 0.74 1.28 1095.00 Abnormal 318.52 34.76 0.69 1.42 256.25 Abnormal Abnormal Abnormal 55 340.95 38.08 0.87 1.25 969.55 Normal 379.38 41.20 0.73 1.81 317.59 Normal Normal Abnormal 56 336.95 40.83 0.82 1.44 1193.05 Normal 356.33 39.14 0.74 1.78 291.63 Normal Normal Normal 57 352.33 42.82 0.82 1.22 1310.34 Normal Normal Normal 58 339.18 40.54 0.80 1.41 1169.05 Normal Normal Normal 59 349.92 41.69 0.80 1.44 1239.16 Normal Normal Normal 60 338.46 40.41 0.80 1.25 1163.38 Normal 356.03 39.28 0.74 1.64 292.59 Normal Normal Normal Table 5.9 VLA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis. Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 1 508.82 52.15 0.65 1.23 2074.92 Normal 298.45 25.90 0.55 1.47 509.92 Normal Normal Normal 2 479.70 51.78 0.68 1.23 2040.71 Normal 257.06 23.02 0.56 1.38 404.00 Abnormal Abnormal Abnormal 3 301.45 36.88 0.77 1.22 1039.89 Abnormal 278.67 25.96 0.59 1.47 514.27 Abnormal Abnormal Abnormal 4 491.78 55.74 3.18 1.65 2148.14 Normal 290.05 25.80 0.56 1.40 510.80 Normal Normal Normal 5 427.92 47.11 0.69 1.26 1715.54 Abnormal 265.61 23.06 0.55 1.39 406.38 Abnormal Abnormal Abnormal 6 519.66 53.00 0.64 1.19 2139.15 Normal Normal Normal 7 469.64 51.70 0.69 1.14 2036.50 Normal Normal Normal (continues) ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 83 Table 5.9 VLA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis (continuation). Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 8 468.67 52.65 0.71 1.25 2111.82 Normal Normal Normal 9 482.12 49.98 0.65 1.36 1904.25 Normal Normal Normal 10 485.64 53.01 0.73 1.23 1996.31 Normal Normal Normal 11 492.10 53.69 0.73 1.26 2049.46 Normal Normal Normal 12 484.49 52.32 0.68 1.11 2087.53 Normal Normal Normal 13 482.09 50.62 0.66 1.18 1954.09 Normal Normal Normal 14 476.58 49.97 0.66 1.19 1902.36 Normal Normal Normal 15 501.54 53.10 0.67 1.27 2157.92 Normal Normal Normal 16 512.68 56.21 0.79 1.47 2099.23 Normal Normal Normal 17 348.08 41.51 0.75 1.28 1328.80 Abnormal 298.45 25.90 0.55 1.47 509.92 Normal Abnormal Normal 22 521.26 52.83 0.64 1.24 2127.64 Normal 285.06 25.46 0.56 1.36 168.78 Normal Normal Normal 23 474.92 50.42 0.67 1.12 1935.67 Normal 279.90 24.90 0.56 1.38 164.75 Abnormal Abnormal Abnormal 24 530.08 51.73 0.62 1.23 2042.73 Normal 274.98 24.26 0.55 1.44 160.04 Abnormal Abnormal Abnormal 25 475.79 52.00 0.69 1.21 2056.75 Normal 269.66 23.78 0.55 1.36 156.50 Abnormal Abnormal Abnormal 26 473.87 49.95 0.66 1.21 1898.09 Normal 290.63 25.65 0.56 1.39 171.28 Normal Normal Normal 27 496.35 51.22 0.65 1.31 1995.27 Normal 303.37 26.30 0.54 1.47 175.92 Normal Normal Normal 29 512.61 54.32 0.67 1.16 2260.87 Normal 234.17 21.02 0.56 1.31 138.52 Normal Normal Normal 31 492.72 52.95 0.72 1.17 1993.82 Normal 291.87 26.61 0.61 1.48 176.04 Normal Normal Normal 33 550.17 55.24 0.63 1.38 2330.62 Abnormal 290.16 25.66 0.56 1.45 171.17 Normal Abnormal Normal 35 538.86 55.01 0.64 1.20 2165.03 Abnormal 278.36 24.23 0.55 1.32 160.04 Normal Abnormal Abnormal 36 550.17 55.24 0.63 1.38 2330.62 Abnormal 272.21 23.90 0.55 1.26 157.51 Normal Abnormal Normal (continues) ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 84 Table 5.9 VLA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis (continuation). Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 37 485.82 50.81 0.66 1.28 1965.00 Normal 276.95 24.91 0.57 1.30 165.23 Abnormal Abnormal Normal 38 517.84 53.95 0.66 1.20 2222.94 Normal 269.60 23.85 0.56 1.31 157.49 Normal Normal Normal 39 459.06 49.96 0.68 1.18 1904.00 Abnormal 272.68 24.28 0.56 1.30 160.38 Normal Abnormal Abnormal 40 464.82 52.64 0.71 1.13 2114.00 Abnormal 271.60 24.11 0.56 1.28 159.25 Normal Abnormal Normal 42 488.79 52.18 0.72 1.20 1933.30 Normal 279.34 25.05 0.56 1.41 165.93 Normal Normal Normal 43 492.38 53.24 0.73 1.21 2019.77 Normal 274.66 24.33 0.56 1.32 160.95 Normal Normal Normal 44 492.38 53.24 0.73 1.21 2019.77 Normal 286.08 25.02 0.55 1.52 165.68 Normal Normal Normal 45 417.66 46.56 0.70 1.25 1649.82 Abnormal 275.08 25.50 0.58 1.38 169.56 Abnormal Abnormal Abnormal 46 460.77 49.16 0.67 1.17 1840.67 Abnormal 288.82 25.32 0.55 1.39 168.95 Normal Abnormal Normal 47 467.12 52.06 0.70 1.19 1950.75 Normal Normal Normal 48 494.45 54.37 0.69 1.22 2259.19 Normal Normal Normal 49 506.97 53.03 0.70 1.28 2001.19 Normal Normal Normal 50 524.33 52.89 0.64 1.21 2129.54 Normal 290.90 25.75 0.56 1.46 508.31 Normal Normal Abnormal 51 444.27 53.38 0.70 1.44 2026.66 Abnormal 279.81 24.89 0.56 1.45 472.46 Abnormal Abnormal Abnormal 52 505.41 53.17 0.66 1.17 2154.58 Normal Normal Normal 53 488.75 51.80 0.67 1.08 2051.17 Normal 294.92 26.38 0.60 1.37 495.99 Normal Normal Normal 54 502.57 53.96 0.68 1.17 2219.37 Normal 244.83 22.03 0.57 1.34 369.31 Abnormal Abnormal Abnormal 55 427.57 46.11 0.73 1.43 1511.17 Normal 287.00 26.50 0.58 1.33 535.00 Normal Normal Normal 56 490.36 52.51 0.67 1.17 2104.20 Normal 299.45 26.54 0.60 1.57 501.25 Normal Normal Normal 57 487.73 52.36 0.72 1.30 1949.30 Normal Normal Normal 58 489.04 52.19 0.67 1.13 2073.14 Normal Normal Normal (continues) ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 85 Table 5.9 VLA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis (continuation). Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 59 495.31 54.25 0.74 1.26 2091.85 Normal Normal Normal 60 472.95 51.18 0.68 1.10 1996.91 Normal 292.74 26.53 0.61 1.34 502.08 Normal Normal Normal Table 5.10. SA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis. Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 1 397.03 30.32 0.48 1.22 225.54 Normal 384.64 25.74 0.42 1.20 507.80 Normal Normal Normal 2 454.49 34.16 0.47 1.13 264.03 Normal 355.12 24.15 0.43 1.26 445.65 Abnormal Abnormal Abnormal 3 385.89 28.96 0.48 1.16 207.52 Abnormal 398.84 26.47 0.42 1.08 534.07 Normal Abnormal Abnormal 4 507.49 37.63 0.47 1.21 301.12 Normal 425.40 29.02 0.43 1.28 660.29 Normal Normal Normal 5 296.01 23.55 0.50 1.11 160.15 Abnormal 333.98 23.03 0.43 1.23 403.36 Abnormal Abnormal Abnormal 6 404.03 30.17 0.55 1.33 212.87 Normal Normal Normal 7 455.60 33.55 0.46 1.18 253.50 Normal Normal Normal 8 459.33 34.05 0.47 1.17 262.51 Normal Normal Normal 9 400.45 31.51 0.53 1.28 224.27 Normal Normal Normal 10 401.58 30.46 0.48 1.09 225.26 Normal Normal Normal 11 412.60 31.69 0.48 1.15 233.35 Normal Normal Normal 12 417.43 30.67 0.46 1.20 225.12 Normal Normal Normal 13 409.49 31.54 0.63 1.37 219.02 Normal Normal Normal 14 415.96 31.50 0.55 1.29 222.99 Normal Normal Normal (continues) ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 86 Table 5.10. SA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis (continuation). Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 15 460.35 32.56 0.45 1.43 243.57 Normal Normal Normal 16 416.10 32.37 0.49 1.19 243.04 Normal Normal Normal 17 406.27 31.33 0.48 1.22 234.72 Normal 384.64 25.74 0.42 1.20 507.80 Normal Normal Normal 22 512.05 37.26 0.46 1.29 297.46 Normal 418.45 27.82 0.42 1.13 596.82 Normal Normal Normal 23 418.13 31.84 0.48 1.16 237.11 Normal 394.41 26.24 0.42 1.18 530.12 Normal Normal Abnormal 24 398.16 29.60 0.47 1.26 213.05 Normal 384.87 25.85 0.42 1.21 510.13 Abnormal Abnormal Abnormal 25 489.31 36.09 0.46 1.26 279.47 Normal 416.92 27.67 0.42 1.22 586.65 Normal Normal Abnormal 26 426.14 32.14 0.48 1.13 241.15 Normal 394.00 26.51 0.45 1.27 499.79 Normal Normal Normal 27 342.76 26.95 0.49 1.08 187.99 Abnormal 392.91 27.18 0.51 1.39 480.51 Normal Abnormal Normal 29 502.02 34.66 0.45 1.29 268.89 Normal 389.55 26.95 0.50 1.38 476.40 Normal Normal Normal 31 406.96 30.26 0.47 1.13 223.17 Normal 395.34 26.44 0.42 1.14 531.85 Normal Normal Normal 33 480.71 34.55 0.46 1.45 267.20 Normal 401.91 26.49 0.42 1.24 539.00 Normal Normal Normal 35 453.11 33.50 0.47 1.21 257.81 Normal 410.73 27.53 0.42 1.14 585.41 Normal Normal Abnormal 36 480.71 34.55 0.46 1.45 267.20 Normal 399.12 27.02 0.43 1.17 563.41 Normal Normal Normal 37 390.25 31.03 0.50 1.20 221.87 Abnormal 387.20 26.09 0.42 1.17 184.19 Normal Abnormal Normal 38 495.26 36.15 0.46 1.20 285.89 Normal 405.51 27.42 0.46 1.23 193.51 Normal Normal Normal 39 401.02 30.04 0.47 1.15 219.09 Abnormal 373.65 25.27 0.43 1.21 176.94 Abnormal Abnormal Abnormal 40 405.33 31.68 0.49 1.11 232.24 Normal 362.77 24.48 0.42 1.17 455.82 Abnormal Abnormal Normal 42 444.57 32.54 0.47 1.16 249.22 Normal 406.77 26.98 0.42 1.19 558.18 Normal Normal Normal 43 443.78 32.31 0.46 1.09 245.97 Normal 409.70 27.63 0.45 1.29 544.99 Normal Normal Normal 44 371.28 28.71 0.52 1.15 202.48 Normal 409.52 27.44 0.42 1.23 573.38 Normal Normal Normal 45 397.18 29.97 0.48 1.21 216.50 Abnormal 395.63 26.67 0.42 1.31 546.47 Normal Abnormal Abnormal (continues) ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 87 Table 5.10. SA geometric dimensions of segmented structures and respective Bayesian classification results and comparison with clinical diagnosis (continuation). Patient Number Stress Rest Final Algorithm Classification Clinical Diagnosis Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification Perimeter Equivalent Spherical Radius Roundness Elongation Number of Pixels Algorithm Classification 46 426.22 31.48 0.47 1.24 233.52 Normal 378.90 26.90 0.42 1.13 492.34 Normal Normal Normal 47 475.62 34.92 0.46 1.30 268.97 Normal Normal Normal 48 467.22 33.92 0.46 1.33 260.68 Normal Normal Normal 49 458.93 34.75 0.48 1.19 260.06 Normal Normal Normal 50 381.71 30.46 0.50 1.14 217.35 Abnormal 371.37 25.25 0.43 1.20 486.38 Abnormal Abnormal Abnormal 51 380.53 30.35 0.50 1.18 220.38 Abnormal 379.45 25.45 0.42 1.19 495.80 Normal Abnormal Abnormal 52 477.98 34.26 0.45 1.33 262.77 Normal Normal Normal 53 438.73 33.75 0.48 1.19 258.05 Normal 377.68 25.36 0.42 1.19 489.27 Normal Normal Normal 54 391.61 29.76 0.48 1.11 216.34 Abnormal 336.69 23.21 0.43 1.19 410.33 Abnormal Abnormal Abnormal 55 343.54 27.08 0.50 1.19 190.48 Abnormal 414.23 27.34 0.42 1.12 574.06 Normal Abnormal Normal 56 401.75 32.49 0.54 1.28 229.94 Normal 408.87 27.66 0.46 1.23 546.06 Normal Normal Normal 57 345.04 26.43 0.48 1.10 185.56 Abnormal Abnormal Normal 58 513.18 37.91 0.50 1.23 292.25 Normal Normal Normal 59 419.75 32.31 0.52 1.19 233.25 Normal Normal Normal 60 472.95 33.81 0.45 1.30 255.53 Normal 404.75 26.83 0.42 1.14 551.06 Normal Normal Normal ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 94 framework, since they solve global and local deformations sequentially through a faster and efficient algorithm. These methods enabled the formation of a template myocardial perfusion SPECT image and its coronary artery mapping. Segmentation algorithm validation was performed using Dice’s coefficient. The comparison of segmented images using ITK automatic segmentation method, Otsu method (3 levels), k-means (3 clusters), region growing and level set methods, against two different gold standards demonstrated k-means as the most robust method. Besides this segmentation method, post-processing image techniques were used. Noise and low level details were overwhelmed and LV segmentation was not distorted by hypertrophied right ventricle myocardium or retention of tracer in the lung(s) or breast activity. However, Dice’s coefficient values of 0.80 and 0.69 means the segmentation methods needs to be optimized. Hereafter, the computational solution presented, consisting on (1) the segmentation of medical patient’s exams, (2) respective registration with template SPECT image, (3) computation of related geometric dimensions, (4) statistical analysis and its classification based on Bayesian theory, demonstrated reasonable robustness. Sensitivity value of 70% and mean error ratio of 12,4% leads to the necessity of optimize the registration and classification methods used. Precision and accuracy parameters have demonstrated the capacity of 83% and 88%, such as specificity presented a performance measure of 95%. Thus, it was presented a good classification performance concerning correct decisions and relevant detections. 6.2. Future works The continuous development and optimization of this computational solution with higher values of classifier evaluation is the priority objective. It is pretended to realize more extensive experimentation of different registration components and respective parameter values, to optimize registration methods. Additionally, image dataset must be augmented to a bigger number of patients, with higher intervariability. Besides the optimization of registration and segmentation techniques used and the reduction of computer processing-time, there are several aspects that can be introduced in this computational solution such as: (1) computation of 3-D coronary artery mapping of template myocardial perfusion and 3-D registration with ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 95 patient’s exams, (2) generating more relevant information as detect the myocardial perfusion disease, (3) informing the clinical professional about the defect percentage of myocardial perfusion for each exam, when compared to template myocardial perfusion uptake ratio, (4) integrate image registration results with electrocardiographic signals, (5) modeling the registered images in 3-D to provide a better visual evaluation and (6) develop a user guide interface. Therefore, it is pretended to contribute to a mathematical grounded and effective diagnosis, monitoring of disease development such as planning of treatments or surgeries. This computational solution will become both physician and medical activity easier and more efficient, through the development, optimization, test, use, comparison and validation of the developed algorithms. ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 96 ANALYSIS OF GATED MYOCARDIAL PERFUSION SPECT IMAGES USING COMPUTATIONAL IMAGE REGISTRATION TECHNIQUES 97 References 1. ZANZONICO, Pat. Basic sciences of nuclear medicine. Heidelberg: Springer, 2011. 2. MUEHLLEHNER, Gerd; KARP, Joel S. Positron emission tomography. Physics in medicine and biology, 2006, 51.13: R117. 3. JASZCZAK, Ronald Jack. The early years of single photon emission computed tomography (SPECT): an anthology of selected reminiscences. Physics in medicine and biology, 2006, 51.13: R99. 4. 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