Persistent homology of tumor CT scans is associated with survival in lung cancer

Abstract

Purpose: Radiomics, the objective study of nonvisual features in clinical imaging, has been useful in informing decisions in clinical oncology. However, radiomics currently lacks the ability to characterize the overall topological structure of the data. This niche can be filled by persistent homology, a form of topological data analysis that analyzes high-level structure. We hypothesized that persistent homology features quantified using cubical complexes could be extracted from lung tumor scans and related to survival.

Methods: We obtained segmented computed tomography (CT) lung scans (n = 565) from the NSCLC-Radiomics and NSCLC-Radiogenomics datasets in The Cancer Imaging Archive. These scans are three-dimensional images whose pixel intensity corresponds to a number of Hounsfield units. Cubical complexes are a topological image analysis method that effectively analyzes the number of topological features in an image as the image is thresholded at different intensities. We calculated a novel output called a feature curve by plotting the number of zero-dimensional (0D) topological features counted from the cubical complex filtration against each Hounsfield value. This curve's first moment of distribution was utilized as a summary statistic to show association with survival in a Cox proportional hazards model. We hypothesized that persistent homology features quantified using cubical complexes could be extracted from lung tumor scans and related to survival.

Results: After controlling for tumor image size, age, and stage, the first moment of the 0D topological feature curve was associated with poorer survival (HR = 1.118; 95% CI = 1.026-1.218; p = 0.01). The patients in our study with the lowest first moment scores had significantly better survival (1238 days; 95% CI = 936-1599) compared to the patients with the highest first moment scores (429 days; 95% CI = 326-601; p = 0.0015).

Conclusions: We have shown that persistent homology can generate useful clinical correlates from tumor CT scans. Our 0D topological feature curve statistic predicts survival in lung cancer patients. This novel statistic may be used in tandem with standard radiomics variables to better inform clinical oncology decisions.

Keywords: computed tomography; lung Cancer; persistent homology; radiomics; topological data analysis; tumor Imaging.