The 2019 mathematical oncology roadmap.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

The accuracy of computer-based diagnostic tools for the identification of concurrent genetic disorders.

The increasing use of next-generation sequencing, especially clinical exome sequencing, has revealed that individuals having two coexisting genetic conditions are not uncommon occurrences. This pilot study evaluates the efficacy of two methodologically distinct computational differential diagnosis generating tools-FindZebra and SimulConsult-in identifying multiple genetic conditions in a single patient. Clinical query terms were generated for each of 15 monogenic disorders that were effective in resulting in the top 10 list of differential diagnoses for each of the 15 monogenic conditions when entered into these bioinformatics tools. Then, the terms of over 125 pairings of these conditions were entered using each tool and the resulting list of diagnoses evaluated to determine how often both diagnoses of a pair were represented in that list. Neither tool was successful in identifying both members of a pair of conditions in greater than 40% of test cases. Disorder detection sensitivity was not homogeneous within a tool, with each tool favoring the identification of a subset of genetic conditions. In view of recent exome sequencing data showing an unexpectedly high prevalence of coexistent monogenic conditions, the results from this pilot study highlight a need for the development of computational tools designed to effectively generate differential diagnoses with consideration of the possibility of coexisting conditions.

Trends in Ophthalmological Patents, 2005-2020.

Purpose: Technological development drives the optimization of therapeutics in ophthalmology, but quantifiable and systematic review of such innovation is lacking. To fill this gap, we characterize trends in ophthalmology-related patents in the United States from 2005 to 2020. Methods: Publicly available patent data from the US Patent and Trademark Office was analyzed with the R programming language. Ophthalmology-related patents were identified with a keyword search of their titles and claims text. Temporal trends were assessed with the Mann-Kendall trend test (α = 0.05, two-sided). Results: Of 4.5 million collected patents, some 21,000 (0.5%) were ophthalmology related. The number of annually granted ophthalmology patents increased over time (Mann-Kendall test: z = 4.91; P < 0.001), from 619 patents released in 2005 to 2,019 patents in 2020. Patent counts also increased over time for all ophthalmic subspecialties except oculoplastics, with steepest rises in retina (z = 4.91; P < 0.001) and cornea (z = 4.64; P < 0.001). The most cited patents were in biocompatible intraocular implants and implantable controlled-release drug delivery systems, which underscores particular advancement in therapeutic efficacy and safety in devices used in the treatment and management of common yet debilitating eye conditions. Conclusion: This exploratory analysis reveals hotspots for ophthalmology-related innovation in the United States that may predict current and future growth trends in device development and pharmacologic advancement in ophthalmology, paving the way for more diverse and effective treatment options for preserving vision.

Temporal Trends in the United States Patent Landscape: Innovation in Cardiology Across Industry and Academia.

Background: Novel approaches to diagnostics and therapeutics in medical care reflect the scientific community's evolving understanding of disease states and their clinical implications. Marketable and valuable innovations are generally patented for protection of intellectual property. Here, we explore the landscape of cardiology-related patents in the United States. Methods: All United States patents granted between 2005 and 2020 were included in this study. Keywords filtering was used to identify patents related to cardiovascular medicine. Statistical inference was conducted with the Mann-Kendall trend and analysis of variance tests. The results in this report are entirely reproducible with Python and R scripts available in a publicly accessible repository. Results: Of the 4,453,733 patents issued by the USPTO between 2005 and 2020, 31,048 (0.7%) were identified as cardiology-related patents. We identified the top 10 institutions within the for-profit and not-for-profit categories that were assigned the most cardiology-related patents in this time period. Distributions of number of patents per inventor were heavily right-skewed, with a small number of inventors responsible for a large number of patents each. Patents in the cardiac imaging subgroup took the longest to gain approval after submission (median delay: 3.6 years). Conclusions: By studying the patent universe, we are able to identify underexplored areas within cardiovascular medicine. Obstacles such as long delays between patent application and approval can hamper innovation within a field. As a next step, we aim to use these results to predict the next area within cardiovascular medicine to undergo explosive research and innovation.

Clinical Nomogram Using Novel Computed Tomography-Based Radiomics Predicts Survival in Patients With Non-Small-Cell Lung Cancer Treated With Stereotactic Body Radiation Therapy.

PURPOSE: Improved 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 persistent homology (PHOM) score, the radiomic quantification of solid tumor topology, as a solution. MATERIALS AND METHODS: Patients diagnosed with stage I or II NSCLC primarily treated with stereotactic body radiation therapy (SBRT) were selected (N = 554). The PHOM score was calculated for each patient's pretreatment computed tomography scan (October 2008-November 2019). PHOM score, age, sex, stage, Karnofsky Performance Status, Charlson Comorbidity Index, and post-SBRT chemotherapy were predictors in the Cox proportional hazards models for OS and cancer-specific survival. Patients were split into high- and low-PHOM score groups and compared using Kaplan-Meier curves for overall survival (OS) and cumulative incidence curves for cause-specific death. Finally, we generated a validated nomogram to predict OS, which is publicly available at Eashwarsoma.Shinyapps. RESULTS: PHOM score was a significant predictor for OS (hazard ratio [HR], 1.17; 95% CI, 1.07 to 1.28) and was the only significant predictor for cancer-specific survival (1.31; 95% CI, 1.11 to 1.56) in the multivariable Cox model. The median survival for the high-PHOM group was 29.2 months (95% CI, 23.6 to 34.3), which was significantly worse compared with the low-PHOM group (45.4 months; 95% CI, 40.1 to 51.8; P < .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 to 0.296) compared with the low-PHOM group (0.171; 95% CI, 0.123 to 0.218; P = .029). CONCLUSION: The PHOM score is associated with cancer-specific survival and predictive of OS. Our developed nomogram can be used to inform clinical prognosis and assist in making post-SBRT treatment considerations.

Benchmarking R packages for Calculation of Persistent Homology.

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.

TDAstats: R pipeline for computing persistent homology in topological data analysis.

High-dimensional datasets are becoming more common in a variety of scientific fields. Well-known examples include next-generation sequencing in biology, patient health status in medicine, and computer vision in deep learning. Dimension reduction, using methods like principal component analysis (PCA), is a common preprocessing step for such datasets. However, while dimension reduction can save computing and human resources, it comes with the cost of significant information loss. Topological data analysis (TDA) aims to analyze the "shape" of high-dimensional datasets, without dimension reduction, by extracting features that are robust to small perturbations in data. Persistent features of a dataset can be used to describe it, and to compare it to other datasets. Visualization of persistent features can be done using topological barcodes or persistence diagrams (Figure 1). Application of TDA methods has granted greater insight into high-dimensional data (Lakshmikanth et al., 2017); one prominent example of this is its use to characterize a clinically relevant subgroup of breast cancer patients (Nicolau, Levine, & Carlsson, 2011). This is a particularly salient study as Nicolau et al. (2011) used a topological method, termed Progression Analysis of Disease, to identify a patient subgroup with 100% survival using that remains invisible to other clustering methods.