Brain metastases and glioblastoma multiforme are the most aggressive and common brain tumours in adults and they require a different clinical management. Anatomical magnetic resonance imaging (MRI) or clinical history, cannot always clearly distinguish between them. This study describes and verifies the use of magnetic resonance spectroscopy (MRS) and magnetic resonance spectroscopic imaging (MRSI) in combination with MRI for differential diagnosis of glioblastomas and metastases. Feature selection methods are applied to the magnetic resonance (MR) spectra of 121 patients and relevant features are detected. Different classification methods are used to distinguish glioblastoma multiforme and metastasis based on the single-voxel MR spectra, but no reliable differentiation is obtained: the accuracy varies from 50 to 78%. Next, MRSI and MRI data from 10 patients (5 glioblastomas, 5 solitary metastases) are used for differentiation purposes. The combination of multivoxel MR data and MRI data suggests a more clear differentiation between glioblastoma multiforme and brain metastasis. The results are visualized based on nosologic images, which are generated by including spectroscopic information in the segmented MR image. The methodology offers a new way that may support clinicians in decision making.

In this correspondence, several algorithms to compute a lower bound of the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix are described and compared in terms of accuracy and computational efficiency. Exploiting the Toeplitz structure of the considered matrix, new theoretical insights are derived and an efficient implementation of some of the aforementioned algorithms is provided.