In vivo dynamic image characterization of brain tumor growth using singular value decomposition and eigenvalues

This paper presents a dynamic image approach to characterize the growth of brain cancer invasion of tumor gliomas cells using singular value decomposition (SVD) technique. Such a dynamic image is identified by the white and grey matter displayed by magnetic resonance (MR) images of the patient brain taken at different times. SVD components and properties 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 geometrically interprets an ellipsoid transformation, then the higher the eigenvalues, the more of tumor growth is. In vivo SVD dynamic imaging offers a more predictive model to assess the tumor therapy than conventional technologies. Furthermore, an efficient dynamic 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 different times. Finally, SVD image processing results are demonstrated to verify the effectiveness of the applied approach that can be implemented for each individual patient.