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The accurate diagnosis of glioma subtypes is critical for appropriate treatment, but conventional histopathologic diagnosis often exhibits significant intra-observer variability and sampling error. The aim of this study was to investigate whether histogram analysis using an automatically segmented region of interest (ROI), excluding cystic or necrotic portions, could improve the differentiation between low-grade and high-grade gliomas. Thirty-two patients (nine low-grade and 23 high-grade gliomas) were included in this retrospective investigation. The outer boundaries of the entire tumors were manually drawn in each section of the contrast-enhanced T1 -weighted MR images. We excluded cystic or necrotic portions from the entire tumor volume. The histogram analyses were performed within the ROI on normalized apparent diffusion coefficient (ADC) maps. To evaluate the contribution of the proposed method to glioma grading, we compared the area under the receiver operating characteristic (ROC) curves. We found that an ROI excluding cystic or necrotic portions was more useful for glioma grading than was an entire tumor ROI. In the case of the fifth percentile values of the normalized ADC histogram, the area under the ROC curve for the tumor ROIs excluding cystic or necrotic portions was significantly higher than that for the entire tumor ROIs (p < 0.005). The automatic segmentation of a cystic or necrotic area probably improves the ability to differentiate between high- and low-grade gliomas on an ADC map.

We study the phase transitions of a restricted solid-on-solid model coupled to an Ising model, which can be derived from the coupled XY -Ising model. This result is strong evidence that the fully frustrated XY model orders by two separate transitions and that roughening and reconstruction transitions of crystal surfaces occur separately.

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