Abstract
The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US National Library of Medicine and the National Institutes of Health. Seminal papers have initiated and promoted mathematical modeling of cancer and have helped define the field of mathematical oncology (Norton and Simon in J Natl Cancer Inst 58:1735–1741, 1977; Norton in Can Res 48:7067–7071, 1988; Hahnfeldt et al. in Can Res 59:4770–4775, 1999; Anderson et al. in Comput Math Methods Med 2:129–154, 2000. https://doi.org/10.1080/10273660008833042; Michor et al. in Nature 435:1267–1270, 2005. https://doi.org/10.1038/nature03669; Anderson et al. in Cell 127:905–915, 2006. https://doi.org/10.1016/j.cell.2006.09.042; Benzekry et al. in PLoS Comput Biol 10:e1003800, 2014. https://doi.org/10.1371/journal.pcbi.1003800). Following the introduction of undergraduate and graduate programs in mathematical biology, we have begun to see curricula developing with specific and exclusive focus on mathematical oncology. In 2018, 218 articles on mathematical modeling of cancer were published in various journals, including not only traditional modeling journals like the Bulletin of Mathematical Biology and the Journal of Theoretical Biology, but also publications in renowned science, biology, and cancer journals with tremendous impact in the cancer field (Cell, Cancer Research, Clinical Cancer Research, Cancer Discovery, Scientific Reports, PNAS, PLoS Biology, Nature Communications, eLife, etc). This shows the breadth of cancer models that are being developed for multiple purposes. While some models are phenomenological in nature following a bottom-up approach, other models are more top-down data-driven. Here, we discuss the emerging trend in mathematical oncology publications to predict novel, optimal, sometimes even patient-specific treatments, and propose a convention when to use a model to predict novel treatments and, probably more importantly, when not to.
Highlights
1.1 The Past and Present of Mathematical OncologyMathematical modeling in cancer has a long history as reviewed in multiple publications (Araujo and McElwain 2004; Lowengrub et al 2010; Altrock et al 2015; Friedman 2004)
According to PubMed records provided by the US National Library of Medicine and the National Institutes of Health, the number of publications on mathematical modeling of cancer is growing at an exponential rate (Fig. 1)
One of the mainstays of mathematical oncology is modeling of the various oncological treatments including surgery (Hanin et al 2015; Enderling et al 2005), radiation therapy (McAneney and O’Rourke 2007; Kempf et al 2010; Alfonso et al Fig. 1 PubMed query for “Mathematical model” AND (“cancer” OR “tumor”), accessed 3/1/19
Summary
Mathematical modeling in cancer has a long history as reviewed in multiple publications (Araujo and McElwain 2004; Lowengrub et al 2010; Altrock et al 2015; Friedman 2004). As cancer is an umbrella term for more than 100 different diseases with different intrinsic dynamics and unique environmental and ecological niches, mathematical models have begun to focus on the properties of specific cancers such as leukemia (Michor et al 2005) and glioma (Eikenberry et al 2010) or cancers of the breast (Enderling et al 2006), prostate (Swanson et al 2001), or bladder (Bunimovich-Mendrazitsky et al 2008) among many others. Model analysis and numerical simulations demonstrate evolving population level dynamics based on these mechanisms This allows the study of complex biological and mathematical systems, and how perturbations to individual mechanisms or rate constants qualitatively change tumor growth or treatment response. Vis-à-vis the bottom-up approach is the top-down approach, where population level dynamics are used to infer the mechanisms that most likely underlie the observed data With sparse data, this often limits complexity of mathematical oncology models. As many cancer modelers lack access to high-resolution cancer biology or oncology data including independent training and validation data sets, many models are merely academic and not positioned to speculate on optimal therapy
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