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Objectives: This study aimed to assess the value of magnetic resonance perfusion (MR perfusion) and magnetic resonance spectroscopy (MR spectroscopy) in 3.0-Tesla magnetic resonanceimaging (MRI) for differential diagnosis of glioblastoma (GBM) and solitary brain metastasis (SBM). Material and Methods: This retrospective study involved 36 patients, including 24 cases of GBM and 12 of SBM diagnosed using histopathology. All patients underwent a 3.0-Tesla MRI examination with pre-operative MR perfusion and MR spectroscopy. We assessed the differences in age, sex, cerebral blood volume (CBV), relative CBV (rCBV), and the metabolite ratios of choline/N-acetylaspartate (Cho/NAA) and Cho/creatine between the GBM and SBM groups using the Mann–Whitney U-test and Chi-square test. The cutoff value, area under the curve, sensitivity, specificity, positive predictive value, and negative predictive value of the significantly different parameters between these two groups were determined using the receiver operating characteristic curve. Results: In MR perfusion, the CBV of the peritumoral region (pCBV) had the highest preoperative predictive value in discriminating GBM from SBM (cutoff: 1.41; sensitivity: 70.83%; and specificity: 83.33%), followed by the ratio of CBV of the solid tumor component to CBV of normal white matter (rCBVt/n) and the ratio of CBV of the pCBV to CBV of normal white matter (rCBVp/n). In MR spectroscopy, the Cho/NAA ratio of the pCBV (pCho/NAA; cutoff: 1.02; sensitivity: 87.50%; and specificity: 75%) and the Cho/NAA ratio of the solid tumor component (tCho/NAA; cutoff: 2.11; sensitivity: 87.50%; and specificity: 66.67%) were significantly different between groups. Moreover, combining these remarkably different parameters increased their diagnostic utility for distinguishing between GBM and SBM. Conclusion: pCBV, rCBVt/n, rCBVp/n, pCho/NAA, and tCho/NAA are useful indices for differentiating between GBM and SBM. Combining these indices can improve diagnostic performance in distinguishing between these two tumors.

Abstract. For a double array of random elements {V mn ; m ≥ 1, n ≥ 1} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under whichThe weak law results provide con-→ 0 in probability where {Tm; m ≥ 1} and {τn; n ≥ 1} are sequences of positive integer-valued random variables, {kmn; m ≥ 1, n ≥ 1} is an array of positive integers. The sharpness of the results is illustrated by examples.

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