PhD program:: XXXIII

advisor: Roberto Ferretti

Thesis title: Automatic Segmentation, Filtering and Reconstruction of Brain Tumors in MRI Images

The essential goal of this thesis is to analyze and develop some partial differential equation (PDEbased) mathematical models that have shown a significant impact in the field of medical image processing and its role in diagnosis and treatment of lesions. One of the hottest subcategories of medical image processing that we will concentrate on in our work is the segmentation process, particularly, of four brain tumors (meningioma, glioma, glioblastoma and pituitary gland) in 2D MRI images and 3D MRI scans. The research in this field has received a remarkable interest and expansion in the last few decades, since the need of a precise semi-automatic and fully-automatic segmentation process of brain tumors is still a major concern of physicians, radiologists and clinicians; the main reason is that the manual approach is challenging, tedious and time-consuming; specially in case of complex and large amount of images; so we introduce some mathematical models along with their numerical algorithms that significantly reduce the doctors judgment in pre and post-detection and segmentation procedures. Our work involved the following: in the first chapter we reviewed some important concepts and definitions of the area of medical image processing and medical imaging techniques; afterwards, we briefly went over the techniques used in this thesis; here we emphasize that all mathematical models used in our work except for the last chapter were based on the framework of partial differential equations (PDEs). In the second chapter we introduced an efficient PDE-based non-linear image filter used as a pre-processing technique to the segmentation process, since MRI images usually suffer from noise and artifacts, and using a non-linear filter would smoothly facilitate an accurate segmentation process; the filter showed excellent results in the context of MRI images and their segmentation purposes. In the third chapter we discussed four PDE-based segmentation models in which we can semi-automatically segment three types of brain tumors in three different planes (axial, sagittal and coronal) in three different modalities of MRI images (T1-CE, T2 and FLAIR) using an interactive user-interface. In the fourth chapter we dealt with 3D MRI scans, where we aim at reconstructing a 3D shape of the brain tumor (glioblastoma) using three different PDE-based models by segmenting few slices in three different planes using one of the four segmentation models proposed in chapter 2. Unlike the previous chapters, the fifth chapter was based on artificial intelligence techniques, specifically, the field of deep learning, due to its recent boom in medical areas; the purpose of this chapter was to fully-automate all recognition and segmentation processes of brain tumors, and achieve accurate results almost without an intervention by doctors. After all, many advantages and useful real applications can be obtained after the fully- automatic segmentation process, such as, extracting the exact location and boundaries of the tumor, classifying it based on its type, computing its area and circumference in case of 2D image, as well as, volume and surface area in case of 3D reconstruction; such measurements and information about the tumor could be quite valuable for doctors in pre and post-treatment procedures, and highly contribute to surgical planning. The sixth and last chapter we summarized our results and discussed our contribution to the field, and finally we proposed several insights and approaches for a future work.

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