Current Stem Cell Reports

, Volume 5, Issue 1, pp 22–30 | Cite as

Recasting the Cancer Stem Cell Hypothesis: Unification Using a Continuum Model of Microenvironmental Forces

  • Jacob G. Scott
  • Andrew Dhawan
  • Anita Hjelmeland
  • Justin Lathia
  • Anastasia Chumakova
  • Masahiro Hitomi
  • Alexander G. Fletcher
  • Philip K. Maini
  • Alexander R. A. AndersonEmail author
Mathematical Models of Stem Cell Behavior (M Kohandel, Section Editor)
Part of the following topical collections:
  1. Topical Collection on Mathematical Models of Stem Cell Behavior


Purpose of review

Here, we identify shortcomings of standard compartment-based mathematical models of cancer stem-cells, and propose a continuous formalism which includes the tumor microenvironment.

Recent findings

Stem-cell models of tumor growth have provided explanations for various phenomena in oncology including, metastasis, drug- and radio-resistance, and functional heterogeneity in the face of genetic homogeneity. While some of the newer models allow for plasticity, or de-differentiation, there is no consensus on the mechanisms driving this. Recent experimental evidence suggests that tumor microenvironment factors like hypoxia, acidosis, and nutrient deprivation have causative roles.


To settle the dissonance between the mounting experimental evidence surrounding the effects of the microenvironment on tumor stemness, we propose a continuous mathematical model where we model microenvironmental perturbations like forces, which then shape the distribution of stemness within the tumor. We propose methods by which to systematically measure and characterize these forces, and show results of a simple experiment which support our claims.


Cancer stem cell hypothesis Mathematical model Partial differential equations 


Compliance with Ethical Standards

Conflict of Interests

The authors declare no conflicts of interest.


Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jacob G. Scott
    • 1
    • 2
  • Andrew Dhawan
    • 1
    • 3
  • Anita Hjelmeland
    • 4
  • Justin Lathia
    • 5
  • Anastasia Chumakova
    • 5
  • Masahiro Hitomi
    • 1
    • 5
  • Alexander G. Fletcher
    • 6
    • 7
  • Philip K. Maini
    • 2
  • Alexander R. A. Anderson
    • 8
    Email author
  1. 1.Departments of Translational Hematology and Oncology Research and Radiation OncologyCleveland ClinicClevelandUSA
  2. 2.Wolfson Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK
  3. 3.Department of OncologyUniversity of OxfordOxfordUK
  4. 4.Department of Cell, Developmental and Integrative BiologyUniversity of AlabamaBirminghamUSA
  5. 5.Department of Cellular and Molecular Medicine, Lerner Research InstituteCleveland ClinicClevelandUSA
  6. 6.School of Mathematics and StatisticsUniversity of SheffieldSheffieldUK
  7. 7.Bateson CentreUniversity of SheffieldSheffieldUK
  8. 8.Department of Integrated Mathematical OncologyMoffitt Cancer Center and Research InstituteTampaUSA

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