Quantifying U‐Net uncertainty in multi‐parametric MRI‐based glioma segmentation by spherical image projection

Abstract

BackgroundUncertainty quantification in deep learning is an important research topic. For medical image segmentation, the uncertainty measurements are usually reported as the likelihood that each pixel belongs to the predicted segmentation region. In potential clinical applications, the uncertainty result reflects the algorithm's robustness and supports the confidence and trust of the segmentation result when the ground‐truth result is absent. For commonly studied deep learning models, novel methods for quantifying segmentation uncertainty are in demand.PurposeTo develop a U‐Net segmentation uncertainty quantification method based on spherical image projection of multi‐parametric MRI (MP‐MRI) in glioma segmentation.MethodsThe projection of planar MRI data onto a spherical surface is equivalent to a nonlinear image transformation that retains global anatomical information. By incorporating this image transformation process in our proposed spherical projection‐based U‐Net (SPU‐Net) segmentation model design, multiple independent segmentation predictions can be obtained from a single MRI. The final segmentation is the average of all available results, and the variation can be visualized as a pixel‐wise uncertainty map. An uncertainty score was introduced to evaluate and compare the performance of uncertainty measurements.The proposed SPU‐Net model was implemented on the basis of 369 glioma patients with MP‐MRI scans (T1, T1‐Ce, T2, and FLAIR). Three SPU‐Net models were trained to segment enhancing tumor (ET), tumor core (TC), and whole tumor (WT), respectively. The SPU‐Net model was compared with (1) the classic U‐Net model with test‐time augmentation (TTA) and (2) linear scaling‐based U‐Net (LSU‐Net) segmentation models in terms of both segmentation accuracy (Dice coefficient, sensitivity, specificity, and accuracy) and segmentation uncertainty (uncertainty map and uncertainty score).ResultsThe developed SPU‐Net model successfully achieved low uncertainty for correct segmentation predictions (e.g., tumor interior or healthy tissue interior) and high uncertainty for incorrect results (e.g., tumor boundaries). This model could allow the identification of missed tumor targets or segmentation errors in U‐Net. Quantitatively, the SPU‐Net model achieved the highest uncertainty scores for three segmentation targets (ET/TC/WT): 0.826/0.848/0.936, compared to 0.784/0.643/0.872 using the U‐Net with TTA and 0.743/0.702/0.876 with the LSU‐Net (scaling factor = 2). The SPU‐Net also achieved statistically significantly higher Dice coefficients, underscoring the improved segmentation accuracy.ConclusionThe SPU‐Net model offers a powerful tool to quantify glioma segmentation uncertainty while improving segmentation accuracy. The proposed method can be generalized to other medical image‐related deep‐learning applications for uncertainty evaluation.

A neural ordinary differential equation model for visualizing deep neural network behaviors in multi‐parametric MRI‐based glioma segmentation

“…One major issue of currently available deep learning models is the lack of model explainability, that is, the extent to which the internal mechanics of a deep neural network can be explained in human terms from a clinical perspective. The explainability ensures that the networks are driven by (1) deep features that are appropriate for clinical practice and (2) decisions that are clinically defensible 39–43 . Without such model explainability, deep learning algorithms remain a "black box" in implementation.…”