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Noninvasive biomarkers that capture the adenocarcinoma aggressiveness could provide crucial quantitative information for precision medicine to aid clinical decision making. Texture features are known to measure tumor heterogeneity and have been identified as the features having a potential correlation to outcomes in lung adenocarcinomas. Nevertheless, current methods for analyzing texture patterns that arise from local intensity variation are limited to reveal a spatial configuration of the texture structures in 3D thoracic CT images. This lack of an intuitive visualization of the texture of nodules makes understanding the meanings underlying the tumor heterogeneity a challenging problem. In this study, we propose an approach combining a structure-texture image decomposition with a topological data analysis to represent a spatial configuration of the texture of lung adenocarcinoma. The image decomposition aims to split the 3D thoracic CT image into two components, namely, the structure component with the piecewise-smooth part having the global structural information of nodule and the texture component with the locally-patterned oscillating part. We demonstrate the use of topological data analysis to capture architectural features that arise from the texture component. Specifically, using persistent homology of texture components, we compute topological representations of lung adenocarcinomas with the appearance of consolidation on CT images. Applying the method to an example of early-stage lung adenocarcinomas graded with texture features based on the popular algorithm such as gray-level co-occurrence matrix (GLCM), we present that the structure-texture image decomposition model with topological data analysis might be a promising tool in analyzing the tumor heterogeneity in 3D thoracic CT images.
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