The mathematical investigation of cancer began in the 1950s when several investigators set out to explain the age-dependent incidence curves of human cancers. Early milestones were Armitage and Doll's observation that log-log plots of cancer incidence curves were linear, and Knudson's statistical study of retinoblastoma which led to the two-hit hypothesis of tumor suppressor gene inactivation. Subsequent theoretical and experimental work has proven the hypothesis that for most cancer types, the accumulation of several mutations is necessary not only for cancer initiation, progression, and metastatic spread, but also for the emergence of resistance against chemotherapeutics. There is a large and growing mathematical literature on cancer models, but most of the analyses are performed for Markovian models of a homogeneously mixing population of a constant size or for an exponentially growing branching process. The main aim of this proposal is to develop flexible mathematical analyses to understand the changes in predicitons when the cell population is divided into different types of cells, when residence times in the different compartments of the model are not exponential, or when the spatial structure of growing tumors is taken into account. We will also consider the implications of these considerations for tumor heterogeneity, and for the types of cells that are the most likely targets of mutations that initiate disease or treatment failure.

Public Health Relevance

The mutational changes that lead to cancer are not directly observable, so mathematical models are needed to test hypotheses about the mechanisms underlying cancer initiation, progression, and metastasis. Models can also give insights into emergence of reistance to chemotherapy and into the effectiveness of proposed treatments.

National Institute of Health (NIH)
National Institute of General Medical Sciences (NIGMS)
Research Project (R01)
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Special Emphasis Panel (ZGM1-CBCB-5 (BM))
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Brazhnik, Paul
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Duke University
Biostatistics & Other Math Sci
Schools of Arts and Sciences
United States
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Cao, Yangxiaolu; Ryser, Marc D; Payne, Stephen et al. (2016) Collective Space-Sensing Coordinates Pattern Scaling in Engineered Bacteria. Cell 165:620-30
Ryser, Marc D; Worni, Mathias; Turner, Elizabeth L et al. (2016) Outcomes of Active Surveillance for Ductal Carcinoma in Situ: A Computational Risk Analysis. J Natl Cancer Inst 108:
Durrett, R; Foo, J; Leder, K (2016) Spatial Moran models, II: cancer initiation in spatially structured tissue. J Math Biol 72:1369-400
Durrett, Richard; Moseley, Stephen (2015) Spatial Moran Models I. Stochastic Tunneling in the Neutral Case. Ann Appl Probab 25:104-115
Talkington, Anne; Durrett, Rick (2015) Estimating Tumor Growth Rates In Vivo. Bull Math Biol 77:1934-54
Ryser, Marc D; McGoff, Kevin; Herzog, David P et al. (2015) Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies. Epidemics 11:32-47
Foo, Jasmine; Leder, Kevin; Ryser, Marc D (2014) Multifocality and recurrence risk: a quantitative model of field cancerization. J Theor Biol 355:170-84
Aristotelous, Andreas C; Durrett, Richard (2014) Fingering in Stochastic Growth Models. Exp Math 23:465-474
Aristotelous, Andreas C; Durrett, Richard (2014) Chemical evolutionary games. Theor Popul Biol 93:1-13
Liu, Lin; De, Subhajyoti; Michor, Franziska (2013) DNA replication timing and higher-order nuclear organization determine single-nucleotide substitution patterns in cancer genomes. Nat Commun 4:1502

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