Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as deep learning explainability enhancement.
Methods: By hypothesizing that deep feature extraction can be modeled as a spatiotemporally continuous process, we designed a novel deep learning model, neural ODE, in which deep feature extraction was governed by an ODE without explicit expression. The dynamics of 1) MR images after interactions with the deep neural network and 2) segmentation formation can thus be visualized after solving ODE. An accumulative contribution curve (ACC) was designed to quantitatively evaluate each MR image’s utilization by the deep neural network towards the final segmentation results. The proposed Neural ODE model was demonstrated using 369 glioma patients with a 4-modality mp-MRI protocol: T1, contrast-enhanced T1 (T1-Ce), T2, and FLAIR. Three neural ODE models were trained to segment enhancing tumor (ET), tumor core (TC), and whole tumor (WT), respectively, and key MR modalities with significant utilization by deep neural networks were identified based on ACC analysis. Segmentation results by deep neural networks using only the key MR modalities were compared to the ones using all 4 MR modalities.
Results: All neural ODE models successfully illustrated image dynamics as expected. ACC analysis identified T1-Ce as the only key modality in ET and TC segmentations, while both FLAIR and T2 were key modalities in WT segmentation. Compared to the U-Net results using all 4 MR modalities, Dice coefficient of ET (0.784→0.775), TC (0.760→0.758), and WT (0.841→0.837) using the key modalities only had minimal differences without significance. Accuracy, sensitivity, and specificity results demonstrated the same patterns.
Conclusion: The neural ODE model offers a new tool for deep learning model input optimization with enhanced explainability. The presented methodology can be generalized to other medical image-related deep learning applications.
Funding Support, Disclosures, and Conflict of Interest: This work is partially supported by institutional P30 Cancer Center Support Grant (Grant ID: NIH CA014236)