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

Lu Wang,Nan Xu,Jiangdian Song

doi:10.1186/s13244-021-01100-8

Abstract

BackgroundCurrent intra-tumoral heterogeneous feature extraction in radiology is limited to the use of a single slice or the region of interest within a few context-associated slices, and the decoding of intra-tumoral spatial heterogeneity using whole tumor samples is rare. We aim to propose a mathematical model of space-filling curve-based spatial correspondence mapping to interpret intra-tumoral spatial locality and heterogeneity.MethodsA Hilbert curve-based approach was employed to decode and visualize intra-tumoral spatial heterogeneity by expanding the tumor volume to a two-dimensional (2D) matrix in voxels while preserving the spatial locality of the neighboring voxels. The proposed method was validated using three-dimensional (3D) volumes constructed from lung nodules from the LIDC-IDRI dataset, regular axial plane images, and 3D blocks.ResultsDimensionality reduction of the Hilbert volume with a single regular axial plane image showed a sparse and scattered pixel distribution on the corresponding 2D matrix. However, for 3D blocks and lung tumor inside the volume, the dimensionality reduction to the 2D matrix indicated regular and concentrated squares and rectangles. For classification into benign and malignant masses using lung nodules from the LIDC-IDRI dataset, the Inception-V4 indicated that the Hilbert matrix images improved accuracy (85.54% vs. 73.22%, p < 0.001) compared to the original CT images of the test dataset.ConclusionsOur study indicates that Hilbert curve-based spatial correspondence mapping is promising for decoding intra-tumoral spatial heterogeneity of partial or whole tumor samples on radiological images. This spatial-locality-preserving approach for voxel expansion enables existing radiomics and convolution neural networks to filter structured and spatially correlated high-dimensional intra-tumoral heterogeneity.

Highlights

Current intra-tumoral heterogeneous feature extraction in radiology is limited to the use of a single slice or the region of interest within a few context-associated slices, and the decoding of intra-tumoral spatial heterogeneity using whole tumor samples is rare
The voxels on the Hilbert volume and the corresponding pixels in the Hilbert matrix after applying the proposed spatial correspondence mapping are presented in Additional file 1: Appendix Video 1
The results of the above experiments indicated that when transforming images that are commonly visualized in 2D space, such as the slices arranged on axial, coronal, and sagittal planes, the pixel distribution on the corresponding Hilbert matrix is scattered and irregular, difficult to analyze by radiomics or convolutional neural networks

Summary

Introduction

Current intra-tumoral heterogeneous feature extraction in radiology is limited to the use of a single slice or the region of interest within a few context-associated slices, and the decoding of intra-tumoral spatial heterogeneity using whole tumor samples is rare. With the development of data analysis and image scanning, the traditional texture descriptors may not meet the current needs of exploring latent semantics underlying high-resolution radiological images [5, 6]. Intra-tumoral heterogeneity, which reveals the co-existence of multiple subclones with distinct molecular profiles within a single tumor [7, 8], was first proven in the field of molecular image analysis by decoding deeper spatial and temporal heterogeneity. Intra-tumoral heterogeneity provides an opportunity for exploring latent semantic decoding on radiographic images [9]. Represented by the emerging field of radiomics in medical image analysis, decoding intra-tumoral heterogeneity has greatly expanded the knowledge of image phenotypic characteristics [13, 14]

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