Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics

Journal Article (Journal Article)

In this paper, we study a tumor growth equation along with various models for the nutrient component, including a in vitro model and a in vivo model. At the cell density level, the spatial availability of the tumor density n is governed by the Darcy law via the pressure p(n) = n . For finite γ, we prove some a priori estimates of the tumor growth model, such as boundedness of the nutrient density, and non-negativity and growth estimate of the tumor density. As γ → ∞, the cell density models formally converge to Hele-Shaw flow models, which determine the free boundary dynamics of the tumor tissue in the incompressible limit. We derive several analytical solutions to the Hele-Shaw flow models, which serve as benchmark solutions to the geometric motion of tumor front propagation. Finally, we apply a conservative and positivity preserving numerical scheme to the cell density models, with numerical results verifying the link between cell density models and the free boundary dynamical models. γ

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Tang, M; Wang, L; Zhou, Z

Published Date

  • July 1, 2019

Published In

Volume / Issue

  • 24 / 7

Start / End Page

  • 3011 - 3035

International Standard Serial Number (ISSN)

  • 1531-3492

Digital Object Identifier (DOI)

  • 10.3934/dcdsb.2018297

Citation Source

  • Scopus