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Explicit Separation of Growth and Motility in a New Tumor Cord Model

Bulletin of Mathematical Biology volume 71, Article number: 585 (2009) Cite this article

Abstract

We investigate a new model of tumor growth in which cell motility is considered an explicitly separate process from growth. Bulk tumor expansion is modeled by individual cell motility in a density-dependent diffusion process. This model is implemented in the context of an in vivo system, the tumor cord. We investigate numerically microscale density distributions of different cell classes and macroscale whole tumor growth rates as functions of the strength of transitions between classes. Our results indicate that the total tumor growth follows a classical von Bertalanffy growth profile, as many in vivo tumors are observed to do. This provides a quick validation for the model hypotheses. The microscale and macroscale properties are both sensitive to fluctuations in the transition parameters, and grossly adopt one of two phenotypic profiles based on their parameter regime. We analyze these profiles and use the observations to classify parameter regimes by their phenotypes. This classification yields a novel hypothesis for the early evolutionary selection of the metastatic phenotype by selecting against less motile cells which grow to higher densities and may therefore induce local collapse of the vascular network.

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Affiliations

  1. Dept. of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, USA

    Craig J. Thalhauser & Yang Kuang

  2. Department of Neurosurgery Research, Barrow Neurological Institute, St. Joseph’s Hospital and Medical Center, Phoenix, AZ, 85013, USA

    Tejas Sankar & Mark C. Preul

Authors
  1. Craig J. Thalhauser
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  2. Tejas Sankar
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  3. Mark C. Preul
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  4. Yang Kuang
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Correspondence to Yang Kuang.

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Thalhauser, C.J., Sankar, T., Preul, M.C. et al. Explicit Separation of Growth and Motility in a New Tumor Cord Model. Bull. Math. Biol. 71, 585 (2009). https://doi.org/10.1007/s11538-008-9372-8

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  • DOI: https://doi.org/10.1007/s11538-008-9372-8

Keywords

  • Theoretical oncology
  • Tumor cords
  • Mathematical models
  • Reaction–diffusion equations