Partial Information Decomposition as a Multi-Contrast 3D MRI Selection Strategy for Resource-Constrained Deep Neural Network Training in Brain Tumor Segmentation

Technical Summary: Partial Information Decomposition as a Multi-Contrast 3D MRI Selection Strategy

Problem Statement
Multi-contrast 3D MRI is the standard for brain tumor segmentation, as different sequences (T1n, T1c, T2w, T2-FLAIR) capture complementary tissue characteristics. However, utilizing all available sequences imposes significant computational burdens, including increased storage, preprocessing, data transfer, memory usage, and training costs. These costs are amplified in 3D deep learning due to large volume tensors and the need for repeated experiments across architectures and hyperparameters. Current subset selection methods rely on either exhaustive model training (which scales poorly) or single-source relevance measures like mutual information, which often fail to capture synergy—the phenomenon where two sequences are jointly informative even if neither is individually dominant. The core challenge is identifying a compact, high-performing input subset before committing resources to costly downstream model development.

Methodology
The authors propose a pre-training framework based on Partial Information Decomposition (PID) to rank input pairs and select the optimal configuration for downstream training. The pipeline consists of three main stages:

1. Data Preparation and Embedding:

   • Spatially corresponding 32×32×32 patches are sampled from MRI sequences and tumor masks, with 70% of centers drawn from tumor foregrounds.
   • Tumor burden is discretized into classes based on the fraction of voxels assigned to edema, enhancing tumor, and necrotic regions.
   • A separate shallow 3D autoencoder is trained for each MRI sequence to reconstruct input patches. The encoders produce 32-dimensional latent vectors, which are then quantized into discrete source codes ($q_m$) using K-means clustering ($K=16$).

2. PID-Based Pair Ranking:

   • For every possible pair of input sequences $(a, b)$ and each tumor region $c$, the framework estimates mutual information from the joint distribution of the quantized source codes and the discretized tumor burden target.
   • Using a bivariate PID framework, the total information is decomposed into:
     • Redundant ($R$): Information provided by both sources.
     • Unique ($U$): Information specific to one source.
     • Synergistic ($S$): Information available only from the joint observation.
   • An aggregate score is calculated for each pair:
     $$\text{Score}(a, b) = \sum_c w_c \left[ I((q_a, q_b); T_c) + \lambda (U^c_{a|b} + U^c_{b|a} + S^c_{ab}) \right]$$
     where $w_c$ is the normalized inverse frequency of positive patches, and $\lambda=0.5$ weights unique and synergistic information relative to redundancy. The pair with the highest score is selected.

3. Downstream Validation:

   • The selected pair is used to train lightweight 3D U-Nets.
   • The study evaluates the framework using the CoRe-BT dataset (132 training, 30 validation, 28 test subjects) across four sequences.
   • Eleven architecturally identical models are trained: one using all four inputs, all six possible two-input combinations, and four single-input models.
   • Performance is measured via patient-level macro-averaged Dice, HD95, sensitivity, and precision. A post-hoc Shapley value analysis is also performed on the full four-input model to independently verify input importance.

Key Results

• Selection Accuracy: The PID framework ranked the T1c + T2-FLAIR pair as the highest-scoring combination (Score: 0.963).
• Segmentation Performance: On the independent test cohort, the T1c + T2-FLAIR configuration achieved a mean Dice score of 0.676, ranking second overall. The full four-input model achieved 0.687.
  • The selected pair retained 98.5% of the full model's mean Dice performance while using only half the input channels.
  • Statistical testing (paired Wilcoxon) showed no significant difference in Dice ($p=0.0505$) or HD95 ($p=0.174$) between the selected pair and the full model, though the study notes limited statistical power due to the small number of pairs.
• Independent Verification: Shapley analysis on the full model independently identified T2-FLAIR and T1c as the most influential inputs, with their pairwise interaction being the strongest. This alignment between the pre-training PID selection and post-hoc model attribution validates the selection strategy.
• Resource Efficiency: The selection process required training only shallow autoencoders and calculating PID scores, avoiding the need to train a separate deep segmentation model for every candidate pair.

Significance and Claims
The paper positions this work as a proof of concept demonstrating the practical value of PID-based pre-training selection for identifying compact, informative MRI input sets. The authors claim that:

1. Pre-training Selection is Viable: It is possible to identify the strongest input configuration before costly 3D model development, significantly reducing resource commitment.
2. Synergy Detection: The PID framework successfully captures synergistic information (joint utility) that standard mutual information methods might overlook, leading to the selection of T1c (enhancing tumor) and T2-FLAIR (edema) which cover distinct but complementary tumor components.
3. Interpretability: The method provides an interpretable metric for feature selection that aligns with clinical imaging tasks and independent model-based attribution (Shapley values).

The authors remain modest regarding their conclusions, acknowledging limitations such as the small dataset size, the restriction to only four input contrasts, and the lack of statistical significance in some pairwise comparisons due to limited power. They suggest future work should evaluate robustness in larger cohorts and with more than four candidate inputs.