Bulletin of Mathematical Biology

, Volume 76, Issue 7, pp 1762–1782 | Cite as

A Multicompartment Mathematical Model of Cancer Stem Cell-Driven Tumor Growth Dynamics

  • Suzanne L. Weekes
  • Brian Barker
  • Sarah Bober
  • Karina Cisneros
  • Justina Cline
  • Amanda Thompson
  • Lynn Hlatky
  • Philip Hahnfeldt
  • Heiko EnderlingEmail author
Original Article


Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis—a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division—we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.


Cancer stem cells Mathematical model Cancer progression  Age structure Compartment model 



This research arose from a summer project and research collaboration between the ICBP Education & Outreach effort of the Center of Cancer Systems Biology, GRI and Worcester Polytechnic Institute as part of the WPI Research Experience for Undergraduates Program. This work was supported by the ASSURE program of the Department of Defense in partnership with the National Science Foundation REU Site program under Award DMS-1004795 (S. Weekes) and the National Cancer Institute under Award Number U54CA149233 (L. Hlatky).


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Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  • Suzanne L. Weekes
    • 1
  • Brian Barker
    • 2
  • Sarah Bober
    • 1
  • Karina Cisneros
    • 3
  • Justina Cline
    • 4
  • Amanda Thompson
    • 5
  • Lynn Hlatky
    • 6
  • Philip Hahnfeldt
    • 6
  • Heiko Enderling
    • 6
    • 7
    Email author
  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Department of MathematicsUniversity of RochesterRochesterUSA
  3. 3.Department of MathematicsDominican UniversityRiver ForestUSA
  4. 4.Department of Mathematics and Computer ScienceCoe CollegeCedar RapidsUSA
  5. 5.Department of MathematicsUniversity of North Carolina at Chapel HillChapel HillUSA
  6. 6.Center of Cancer Systems Biology, GeneSys Research InstituteTufts University School of MedicineBostonUSA
  7. 7.Department of Integrated Mathematical OncologyH. Lee Moffitt Cancer Center & Research InstituteTampaUSA

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