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Mathematical Modeling of the Metastatic Process

  • Jacob G. ScottEmail author
  • Philip Gerlee
  • David Basanta
  • Alexander G. Fletcher
  • Philip K. Maini
  • Alexander R.A. Anderson
Chapter

Abstract

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.

Keywords

Cellular Automaton Circulate Tumor Cell Deterministic Model Cellular Automaton Stereotactic Body Radiation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgment

The authors would like to thank Katya Kadyshevskaya at the Scripps Institute for help in preparing Fig. 9.6. JGS would like to thank the NIH Loan Repayment Program for support. AGF is funded by the EPSRC and Microsoft Research, Cambridge through grant EP/I017909/1. PG, DB, ARAA and JGS gratefully acknowledge funding from the NCI Integrative Cancer Biology Program (ICBP) grant U54 CA113007 and the PM thanks Physical Sciences in Oncology Centers U54 CA143970.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Jacob G. Scott
    • 1
    • 2
    Email author
  • Philip Gerlee
    • 3
    • 4
  • David Basanta
    • 1
  • Alexander G. Fletcher
    • 2
  • Philip K. Maini
    • 2
  • Alexander R.A. Anderson
    • 1
  1. 1.Integrated Mathematical OncologyH. Lee Moffitt Cancer Center and Research InstituteTampaUSA
  2. 2.Wolfson Centre for Mathematical Biology, Mathematical InstituteOxford UniversityOxfordUK
  3. 3.Mathematical Sciences DivisionUniversity of GothenburgGothenburgSweden
  4. 4.Chalmers University of TechnologyGothenburgSweden

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