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.

Agency
National Institute of Health (NIH)
Institute
National Institute of General Medical Sciences (NIGMS)
Type
Research Project (R01)
Project #
5R01GM096190-05
Application #
8496828
Study Section
Special Emphasis Panel (ZGM1-CBCB-5 (BM))
Program Officer
Brazhnik, Paul
Project Start
2010-07-26
Project End
2014-06-30
Budget Start
2013-07-01
Budget End
2014-06-30
Support Year
5
Fiscal Year
2013
Total Cost
$328,061
Indirect Cost
$65,044
Name
Duke University
Department
Biostatistics & Other Math Sci
Type
Schools of Arts and Sciences
DUNS #
044387793
City
Durham
State
NC
Country
United States
Zip Code
27705
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