In Vivo Dynamic Image Characterization of Brain Tumor Growth Using Singular Value Decomposition and Eigenvalues

Abstract

This paper presents a dynamic image approach to characterize the growth of brain cancer invasion of tumor gliomas cells using singular value decomposi-tion (SVD) technique. Such a dynamic image is identi-fied by the white and grey matter displayed by mag-netic resonance (MR) images of the patient brain taken at different times. SVD components and prop-erties have been analyzed for different brain images. It is figured out that the growth of tumor cells is quantized by the SVD eigenvalues. Since SVD geo-metrically interprets an ellipsoid transformation, then the higher the eigenvalues, the more of tumor growth is. In vivo SVD dynamic imaging offers a more pre-dictive model to assess the tumor therapy than con-ventional technologies. Furthermore, an efficient dy-namic white-black indicator of the tumor growth rate is constructed based on the change in the diagonal eigenvalues matrices of two MR images taken at dif-ferent times. Finally, SVD image processing results are demonstrated to verify the effectiveness of the applied approach that can be implemented for each individual patient.