Stochastic differential equation modeling approach for grading astrocytomas on brain MRI images

Abstract

Astrocytomas are among the most prevalent primary brain tumors and are classified into four grades by the World Health Organization. Accurate grading is essential for guiding treatment, as therapeutic strategies depend heavily on tumor grade. This paper presents a new preoperative classification method for astrocytomas, addressing the issue of data scarcity in medical imaging. This work leverages an advanced statistical modeling approach based on stochastic differential equations to analyze post-contrast T1-weighted brain MRI images that require minimal data and offer rapid processing times. In this method, the alpha-stable nature of MRI images is represented by applying a fractional Laplacian filter, and the parameters of the resulting alpha-stable distribution are fed to classifiers to detect the grade of astrocytomas. The method is implemented in both 1D and 2D processing modes, with customized preprocessing for each. Three classification algorithms were evaluated: support vector machine, K-nearest neighbor, and random forest. In the three-class classification task (Grades II-IV), the support vector machine exhibited superior performance, achieving accuracy, sensitivity, and specificity of 98.49%, 98.42%, and 99.23% in 2D mode, and 93.52%, 93.23%, and 96.72% in 1D mode. The results indicate that the proposed framework has the potential to significantly enhance preoperative grading of astrocytomas.

Keywords: Astrocytoma; Brain tumor grading; Innovation model; SDE; Stochastic differential equation.

Fig. 1

Block diagram of the proposed method for grading astrocytomas.

Fig. 2

(a) Post-contrast T1-weighted MRI image of an astrocytoma. (b) Histogram corresponding only to the brain region in part (a). (c) The whitened histogram in 1D mode, obtained from the histogram in part (b). (d) The whitened image in 2D mode. (e) A histogram of the MRI image with a non-zero background in 2D mode. (f) The whitened histogram in 2D mode, obtained from the histogram in part (e).

Fig. 3

Q-Q plots for a sample slice before (a) and after (b) applying the proposed model in 1D mode, and before (c) and after (d) applying the proposed model in 2D mode.

Fig. 4

Mean SHAP values for grade II (a), grade III (b), and grade IV (c) in the context of 1D mode processing.

Fig. 5

Mean SHAP values for grade II (a), grade III (b), and grade IV (c) in the context of 2D mode processing.

Fig. 6

ROC curve analyses using SVM after applying SDE in 1D (a) and 2D (b) modes.

Fig. 7

Confusion matrices for three-class classification using SVM after applying SDE in 1D (a) and 2D (b) modes.

Fig. 8

t-SNE visualization of the model’s classification performance using SVM after applying SDE in 1D (a) and 2D (b) modes.