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IntroductionImproved survival prediction and risk stratification in non-small cell lung cancer (NSCLC) would lead to better prognosis counseling, adjuvant therapy selection, and clinical trial design. We propose the PHOM (persistent homology) score, the radiomic quantification of solid tumor topology, as a solution.MethodsPatients diagnosed with stage I or II NSCLC primarily treated with stereotactic body radiation therapy (SBRT) were selected (n= 554). The PHOM score was calculated on each patient’s pre-treatment CT scan (10/2008 to 11/2019). PHOM score, age, sex, stage, Karnofsky Performance Status (KPS), Charlson-Comorbidity Index (CCI), and post-SBRT chemotherapy were predictors in the Cox proportional hazards models for overall and cancer-specific survival. Patients were split into high and low PHOM score groups compared using Kaplan-Meier curves for overall survival and cumulative incidence curves for cause specific death. Finally, we generated a validated nomogram to predict overall survival, publicly available athttps://eashwarsoma.shinyapps.io/LungCancerTDATest/.ResultsPHOM score was a significant predictor for overall survival (HR: 1.17, 95% CI: 1.07−1.28) and was the only significant predictor for cancer-specific survival (1.31, 95% CI: 1.11−1.56) in the multivariable Cox model. The median survival for the high PHOM group was 29.2 months (95% CI: 23.6−34.3), which was significantly worse compared to the low PHOM group (45.4 months, 95% CI: 40.1−51.8,p <0.001). The high PHOM group had a significantly greater chance of cancer-specific death at post treatment month 65 (0.244, 95%CI: 0.192−0.296) compared to the low PHOM group (0.171, 95% CI: 0.123−0.218,p= 0.029).ConclusionsThe PHOM score is associated with cancer-specific survival and predictive of overall survival. Our developed nomogram can be used to inform clinical prognosis and assist in making post-SBRT treatment considerations.

Several persistent homology software libraries have been implemented in R. Specifically, the Dionysus, GUDHI, and Ripser libraries have been wrapped by the TDA and TDAstats CRAN packages. These software represent powerful analysis tools that are computationally expensive and, to our knowledge, have not been formally benchmarked. Here, we analyze runtime and memory growth for the 2 R packages and the 3 underlying libraries. We find that datasets with less than 3 dimensions can be evaluated with persistent homology fastest by the GUDHI library in the TDA package. For higher-dimensional datasets, the Ripser library in the TDAstats package is the fastest. Ripser and TDAstats are also the most memory-efficient tools to calculate persistent homology.

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.

Lyme disease is one of the most prevalent and fastest growing vector-borne bacterial illnesses in the United States, with over 25,000 new confirmed cases every year. Humans contract the bacterium Borrelia burgdorferi through the bite of the tick Ixodes scapularis. The tick can receive the bacterium from a variety of small mammal and bird species, but the white-footed mouse Peromyscus leucopus is the primary reservoir in the northeastern United States, especially near human settlement. The tick's life cycle and behavior depend greatly on the season, with different stages of tick biting at different times. Reducing the infection in the tick-mouse cycle may greatly lower human Lyme incidence in some areas. However, research on the effects of various mouse-targeted interventions is limited. One particularly promising method involves administering vaccine pellets to white-footed mice through special bait boxes. In this study, we develop and analyze a mathematical model consisting of a system of nonlinear difference equations to understand the complex transmission dynamics and vector demographics in both tick and mice populations. We evaluate to what extent vaccination of white-footed mice can affect Lyme incidence in I. scapularis, and under which conditions this method saves money in preventing Lyme disease. We find that, in areas with high human risk, vaccination can eliminate mouse-tick transmission of B. burgdorferi while saving money.