The Gd-enhanced area is not fully-adjacent to necrosis number of samples to estimate the model parameters

The angiogenesis process that facilitates tumor growth makes new vessels weak and highly permeable. Anti-angiogenic therapies control the development of new capillaries and as a result control and even reduce the size of Gd-enhanced area. Therefore, the Reversine change in the volume of the Gd-enhanced region reflects the impact of anti-angiogenic treatment on the patients and was evaluated in this work. Gram-Schmidt orthogonalization analysis was used as it generates more robust features compared with the conventional methods of MRI feature extraction. In this analysis, the gray levels of the desired tissue in the composite images are always distributed around unity and thus, regardless of the intensities of the original images, normalization is not needed. To develop predictive models of response, single-regression was used to test the correlation between the extracted features and the response to therapy within 1–3 months post-treatment. We used linear regression model which is a model with the minimum number of parameters and potentially highest generalization. Although non-linear models are able to better fit the data, they need a larger and may have relatively poor generalization. The resultant regression coefficients showed that the linear model was appropriate for our goal. Relative change in the Gd-enhanced volume was chosen as a measure of response because it provides a more accurate tumor assessment compared with the other methods such as 1D or 2D or even 3D measurements where volume assessment is based on the major diagonal diameters of the tumor. The standard deviation of the GM histogram was found to be the most significant feature for the prediction of the response to therapy. This was to some extent predictable because the standard deviation of the histogram of a specific ROI represents the heterogeneity of the corresponding cancerous tissue and the more a tumor is heterogeneous, the more dangerous and fatal it is which means there is less chance for being able to treat the tumor. Multiple-regression was also performed to attain a more accurate prediction relative to the single-regression analysis. This is due to the fact that each of the variables used for the regression was predictive of the response and most of them were almost uncorrelated. On the other hand, the GM-std and WMstd were found highly correlated. That is why combining WM-std and GM-std increased the regression coefficient by only 0.02. This is consistent with a finding in where two features were used for prediction. Although both features predicted the response with a good correlation, they were highly correlated and thus multiple-regression analysis did not improve the prediction accuracy. We found that the tumors with necrosis adjacent to the Gdenhanced areas were more likely to respond to treatment relative to the other tumors. This may be due to the fact that the cells surrounding the necrotic areas are influenced by hypoxia which makes them express the highest amount of VEGF among the tumor cells. This leads us to believe that angiogenesis may be the main mechanism behind the growth of these tumors. Consequently, bevacizumab is probably the best treatment in such cases. In addition, we noted that bevacizumab has favorably influenced the tumors without necrosis but this influence is not as strong.

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