Decoding intra-tumoral spatial heterogeneity on radiological images using the Hilbert curve

Area of Science:

• Radiology and Medical Imaging
• Computational Pathology
• Artificial Intelligence in Oncology

Background:

• Current radiological analysis of intra-tumoral heterogeneity is limited, often using single slices or small regions of interest.
• Decoding spatial heterogeneity across entire tumors remains a significant challenge in radiological assessments.
• There is a need for advanced methods to capture and interpret the complex spatial organization within tumors.

Purpose of the Study:

• To propose a novel mathematical model for spatial correspondence mapping using space-filling curves.
• To interpret intra-tumoral spatial locality and heterogeneity using whole tumor samples.
• To develop a method for decoding and visualizing spatial heterogeneity in 3D tumor volumes.

Main Methods:

• A Hilbert curve-based approach was utilized to expand 3D tumor volumes into 2D matrices, preserving voxel spatial locality.
• The method was validated on 3D lung nodule datasets (LIDC-IDRI), axial images, and 3D blocks.
• Dimensionality reduction techniques were applied to visualize the spatial distribution of voxels within the Hilbert matrices.

Main Results:

• Dimensionality reduction of single axial slices resulted in scattered pixel distributions.
• 3D tumor volumes, when mapped to 2D Hilbert matrices, showed regular, concentrated patterns.
• Classification accuracy for benign vs. malignant lung nodules improved significantly (85.54% vs. 73.22%) using Hilbert matrix images with Inception-V4 compared to original CT images.

Conclusions:

• Hilbert curve-based spatial correspondence mapping shows promise for analyzing intra-tumoral heterogeneity in radiological images.
• This spatial-locality-preserving voxel expansion method facilitates the use of radiomics and deep learning for high-dimensional heterogeneity analysis.
• The approach enables improved filtering of structured, spatially correlated features for enhanced tumor characterization and classification.